National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 24 Jun 2024 16:34:44 GMT2024-06-24T16:34:44Z50591Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problemshttp://scholars.ntou.edu.tw/handle/123456789/24670Title: Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems
Authors: Liu, Chein-Shan; Shen, Jian-Hung; Kuo, Chung-Lun; Chen, Yung-Wei
Abstract: This study sets up two new merit functions, which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems. For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less, where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector. 1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues. Simultaneously, the real and complex eigenvectors can be computed very accurately. A simpler approach to the nonlinear eigenvalue problems is proposed, which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly. The real eigenvalues can be computed by the fictitious time integration method (FTIM), which saves computational costs compared to the one-dimensional golden section search algorithm (1D GSSA). The simpler method is also combined with the Newton iteration method, which is convergent very fast. All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
Mon, 01 Jan 2024 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/246702024-01-01T00:00:00ZA Boundary-Type Numerical Procedure to Solve Nonlinear Nonhomogeneous Backward-in-Time Heat Conduction Equationshttp://scholars.ntou.edu.tw/handle/123456789/24530Title: A Boundary-Type Numerical Procedure to Solve Nonlinear Nonhomogeneous Backward-in-Time Heat Conduction Equations
Authors: Chen, Yung-Wei; Shen, Jian-Hung; Chang, Yen-Shen; Chang, Chun-Ming
Abstract: In this paper, an explicit boundary-type numerical procedure, including a constraint-type fictitious time integration method (FTIM) and a two-point boundary solution of the Lie-group shooting method (LGSM), is constructed to tackle nonlinear nonhomogeneous backward heat conduction problems (BHCPs). Conventional methods cannot effectively overcome numerical instability to solve inverse problems that lack initial conditions and take a long time to calculate, even using different variable transformations and regularization techniques. Therefore, an explicit-type numerical procedure is developed from the FTIM and the LGSM to avoid numerical instability and numerical iterations. First, a two-point boundary solution of the LGSM is introduced into the numerical algorithm. Then, the maximum and minimum values of the initial guess value can be determined linearly from the boundary conditions at the initial and final times. Finally, an explicit-type boundary-type numerical procedure, including a boundary value solution and constraint-type FTIM, can directly avoid the numerical iterative problems of BHCPs. Several nonlinear examples are tested. Based on the numerical results shown, this boundary-type numerical procedure using a two-point solution can directly obtain an approximated solution and can achieve stable convergence to boundary conditions, even if numerical iterations occur. Furthermore, the numerical efficiency and accuracy are better than in the previous literature, even with an increased computational time span without the regularization technique.
Sun, 01 Oct 2023 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/245302023-10-01T00:00:00ZAcoustic Field Radiation Prediction and Verification of Underwater Vehicles under a Free Surfacehttp://scholars.ntou.edu.tw/handle/123456789/24546Title: Acoustic Field Radiation Prediction and Verification of Underwater Vehicles under a Free Surface
Authors: Chen, Yung-Wei; Pan, Cheng-Cheng; Lin, Yi-Hsien; Shih, Chao-Feng; Shen, Jian-Hong; Chang, Chun-Ming
Abstract: This study aimed to examine the acoustic field radiated by propellers and underwater vehicles. For the verification of sound radiation in underwater vehicles, numerical methods are widely used in addition to experiments and propeller blade frequencies for calculation and validation. Numerical convergence and accuracy are more important for near-field and far-field problems. This paper uses the boundary element method (BEM) to assess the convergence of the finite volume method (FVM). In this study, the FVM, including the Reynolds-averaged Navier-Stokes method and the Ffowcs Williams-Hawkings (FW-H) acoustic model, is used to investigate the influence of various geometric inflows on the hydrodynamic and noise performance of the propeller. Then, the sound radiation of the FVM is compared with the BEM at the far field to determine the number of meshed elements. Furthermore, spectral analysis is being conducted to examine the noise generated by the underwater vehicle and propeller. The objective is to investigate the influence of the free surface on propeller efficiency. After verifying the numerical simulation, the results indicate that a relationship can be established between water pressure and propeller thrust under specific conditions. This relationship can be used to estimate the magnitude of propeller thrust at different water depths. The simulated results of propeller thrust, torque coefficient, propulsion efficiency, and sound radiation in this study are consistent with experimental values. This demonstrates the accuracy and practicality of the findings of numerical procedures in engineering applications.
Sun, 01 Oct 2023 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/245462023-10-01T00:00:00ZA Complete Procedure for a Constraint-Type Fictitious Time Integration Method to Solve Nonlinear Multi-Dimensional Elliptic Partial Differential Equationshttp://scholars.ntou.edu.tw/handle/123456789/23689Title: A Complete Procedure for a Constraint-Type Fictitious Time Integration Method to Solve Nonlinear Multi-Dimensional Elliptic Partial Differential Equations
Authors: Chen, Yung-Wei; Shen, Jian-Hung; Chang, Yen-Shen; Tan, Ching-Chuan
Abstract: In this paper, an efficient and straightforward numerical procedure is constructed to solve multi-dimensional linear and nonlinear elliptic partial differential equations (PDEs). Although the numerical procedure for the constraint-type fictitious time integration method overcomes the numerical stability problem, the parameter's definition, numerical accuracy and computational efficiency have not been resolved, and the lack of initial guess values results in reduced computational efficiency. Therefore, the normalized two-point boundary value solution of the Lie-group shooting method is proposed and considered in the numerical procedure to avoid the problem of the initial guess value. Then, a space-time variable, including the minimal fictitious time step and convergence rate factor, is introduced to study the relationship between the initial guess value and convergence rate factor. Some benchmark numerical examples are tested. As the results show, this numerical procedure using the normalized boundary value solution can significantly converge within one step, and the numerical accuracy is better than that demonstrated in the previous literature.
Sun, 01 Jan 2023 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/236892023-01-01T00:00:00ZNonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Methodhttp://scholars.ntou.edu.tw/handle/123456789/23693Title: Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method
Authors: Liu, Chein-Shan; El-Zahar, Essam R.; Chen, Yung-Wei
Abstract: How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations (NAEs). This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms. We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system. Through the maximal orthogonal projection concept, to minimize a merit function within a selected interval of splitting parameters, the optimal parameters can be quickly determined. In each step, a linear system is solved by the Gaussian elimination method, and the whole iteration procedure is convergent very fast. Several numerical tests show the high performance of the optimal split-linearization iterative method (OSLIM).
Sun, 01 Jan 2023 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/236932023-01-01T00:00:00ZA Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm-Liouville Problemshttp://scholars.ntou.edu.tw/handle/123456789/23126Title: A Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm-Liouville Problems
Authors: Liu, Chein-Shan; Chang, Jiang-Ren; Shen, Jian-Hung; Chen, Yung-Wei
Abstract: In the paper, we transform the general Sturm-Liouville problem (SLP) into two canonical forms: one with the homogeneous Dirichlet boundary conditions and another with the homogeneous Neumann boundary conditions. A boundary shape function method (BSFM) was constructed to solve the SLPs of these two canonical forms. Owing to the property of the boundary shape function, we could transform the SLPs into an initial value problem for the new variable with initial values that were given definitely. Meanwhile, the terminal value at the right boundary could be entirely determined by using a given normalization condition for the uniqueness of the eigenfunction. In such a manner, we could directly determine the eigenvalues as the intersection points of an eigenvalue curve to the zero line, which was a horizontal line in the plane consisting of the zero values of the target function with respect to the eigen-parameter. We employed a more delicate tuning technique or the fictitious time integration method to solve an implicit algebraic equation for the eigenvalue curve. We could integrate the Sturm-Liouville equation using the given initial values to obtain the associated eigenfunction when the eigenvalue was obtained. Eight numerical examples revealed a great advantage of the BSFM, which easily obtained eigenvalues and eigenfunctions with the desired accuracy.
Sat, 01 Oct 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/231262022-10-01T00:00:00ZTo Solve Forward and Backward Nonlocal Wave Problems with Pascal Bases Automatically Satisfying the Specified Conditionshttp://scholars.ntou.edu.tw/handle/123456789/22337Title: To Solve Forward and Backward Nonlocal Wave Problems with Pascal Bases Automatically Satisfying the Specified Conditions
Authors: Liu, Chein-Shan; Chang, Chih-Wen; Chen, Yung-Wei; Shen, Jian-Hung
Abstract: In this paper, the numerical solutions of the backward and forward non-homogeneous wave problems are derived to address the nonlocal boundary conditions. When boundary conditions are not set on the boundaries, numerical instability occurs, and the solution may have a significant boundary error. For this reason, it is challenging to solve such nonlinear problems by conventional numerical methods. First, we derive a nonlocal boundary shape function (NLBSF) from incorporating the Pascal triangle as free functions; hence, the new, two-parameter Pascal bases are created to automatically satisfy the specified conditions for the solution. To satisfy the wave equation in the domain by the collocation method, the solution of the forward nonlocal wave problem can be quickly obtained with high precision. For the backward nonlocal wave problem, we construct the corresponding NLBSF and Pascal bases, which exactly implement two final time conditions, a left-boundary condition and a nonlocal boundary condition; in addition, the numerical method for the backward nonlocal wave problem under two-side, nonlocal boundary conditions is also developed. Nine numerical examples, including forward and backward problems, are tested, demonstrating that this scheme is more effective and stable. Even for boundary conditions with a large noise at final time, the solution recovered in the entire domain for the backward nonlocal wave problem is accurate and stable. The accuracy and efficiency of the method are validated by comparing the estimation results with the existing literature.
Thu, 01 Sep 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/223372022-09-01T00:00:00ZPeriodic Orbits of Nonlinear Ordinary Differential Equations Computed by a Boundary Shape Function Methodhttp://scholars.ntou.edu.tw/handle/123456789/22156Title: Periodic Orbits of Nonlinear Ordinary Differential Equations Computed by a Boundary Shape Function Method
Authors: Liu, Chein-Shan; Chang, Chih-Wen; Chen, Yung-Wei; Chang, Yen-Shen
Abstract: In the paper, we determine the period of an n-dimensional nonlinear dynamical system by using a derived formula in an (n + 1)-dimensional augmented space. To form a periodic motion, the periodic conditions in the state space and nonlinear first-order differential equations constitute a special periodic problem within a time interval with an unknown length. Two periodic problems are considered: (a) boundary values are given and (b) boundary values are unknown. By using the shape functions, a boundary shape function method (BSFM) is devised to obtain an initial value problem with the initial values of the new variables given. The unknown terminal values of the new variables and period are determined by two iterative algorithms for the case (a) and one iterative algorithm for the case (b). The periodic solutions obtained from the BSFM satisfy the periodic conditions automatically. For the numerical example, the computed order of convergence displays the merit of the BSFM. For the sake of comparison, the iterative algorithms based on the shooting method for cases (a) and (b) were developed by directly implementing the Poincare map into the fictitious time-integration method to determine the period. The BSFM is better than the shooting method in terms of convergence speed, accuracy, and stability.
Fri, 01 Jul 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/221562022-07-01T00:00:00ZResearch on Optimal Model of Maritime Search and Rescue Route for Rescue of Multiple Distress Targetshttp://scholars.ntou.edu.tw/handle/123456789/21548Title: Research on Optimal Model of Maritime Search and Rescue Route for Rescue of Multiple Distress Targets
Authors: Ho, Wen-Chih; Shen, Jian-Hung; Liu, Chung-Ping; Chen, Yung-Wei
Abstract: Coastal countries began to develop green energy, and offshore wind power equipment in coastal areas was gradually built. Since coastal wind power generation often requires carrying out maintenance between wind turbines with the assistance of service operation vessels, this situation may cause coastal areas to be prone to people falling into the water. However, traditional maritime search and rescue plans take a long time to gather information from man overboard incidents. In order to minimize injuries to people in distress, the maritime search and rescue process must be as short as possible. Despite that all the search and rescue plans are based on the concept of the shortest path, the efficient plans must not only consider the distance but also consider the cost of search and rescue. Therefore, this study established a set of practices applicable to the on-site commander (OSC) to dispatch rescue ships, as well as the planning of maritime search and rescue route models. Based on the easy-to-observe state of the target in distress, the model is analyzed and calculated by Floyd-Warshall algorithm and Grey relational analysis so as to sort the rescue plan and optimize the effect of the search and rescue route at sea. According to the simulation analysis, when the man overboard incident occurs in the coastal area, the OSC can immediately use this model to plan the best search and rescue route and dispatch a reasonable number of rescue ships.
Fri, 01 Apr 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/215482022-04-01T00:00:00ZA Non-Iteration Solution for Solving the Backward-in-Time Two-Dimensional Burgers' Equation with a Large Reynolds Numberhttp://scholars.ntou.edu.tw/handle/123456789/23625Title: A Non-Iteration Solution for Solving the Backward-in-Time Two-Dimensional Burgers' Equation with a Large Reynolds Number
Authors: Chang, Yen-Shen; Chen, Yung-Wei; Liu, Chein-Shan; Chang, Jiang-Ren
Abstract: This article proposes a noniteration solution based on the Lie-group shooting method (LGSM) to solve the backwardin-time two-dimensional Burgers' equation with a large Reynolds number. The backward problem is famous for seriously ill-posed cases because the solution is generally unstable and highly dependent on the input data. Small perturbations in the input data, such as random errors inherent to the measurements in the analysis, can cause large oscillations in the solution. To handle a large Reynolds number under long time spans, it is very difficult to integrate towards the time direction. To avoid time integration and numerical iteration, the noniteration vector solution based on a two-point equation of the LGSM, including the initial and final conditions and boundary conditions (BCs) at the initial and terminal times, can be constructed. When the vector solution can be obtained from the ratios of the wave fronts on the BCs at the initial and terminal times, this solver can avoid the numerical iteration and numerical divergence of the conventional LGSM. Two benchmark examples in one and two variables are examined to illustrate the performance of the proposed method. The numerical results of this research are very consistent with the exact solutions when considering disturbances from noisy data. Even when the Reynolds number reaches 10E12, from the noisy final and boundary data, the noniteration solution can efficiently address the nonlinear Burgers' problem with or without disturbances. This method does not use any transformation techniques, iterative processes, or regularization processes to avoid numerical instability. Hence, a noniterative solution is more stable and accurate for the unsteady nonlinear Burgers' equation than currently used methods.
Sat, 01 Jan 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/236252022-01-01T00:00:00ZNumerical and Approximate Analytic Solutions of Second-order Nonlinear Boundary Value Problemshttp://scholars.ntou.edu.tw/handle/123456789/23716Title: Numerical and Approximate Analytic Solutions of Second-order Nonlinear Boundary Value Problems
Authors: Liu, Chein-Shan; Shen, Jian-Hung; Chen, Yung-Wei
Abstract: The shooting method consists of guessing unknown initial values, transforming a second-order nonlinear boundary value problem (BVP) to an initial value problem and integrating it to obtain the values at the right end to match the specified boundary condition, which acts as a target equation. In the shooting method, the key issue is accurately solving the target equation to obtain highly precise initial values. Due to the implicit and nonlinear property, we develop a generalized derivative-free Newton method (GDFNM) to solve the target equation, which offers very accurate initial values. Numerical examples are examined to show that the shooting method together with the GDFNM can generate a very accurate solution. Additionally, the GDFNM can successfully solve the three-point nonlinear BVPs with high accuracy. A new splitting-linearizing method is developed to express the approximate analytic solutions of nonlinear BVPs in terms of elementary functions, which adopts the Lyapunov technique by inserting a dummy parameter into the governing equation and the power series solution. Then, linearized differential equations are sequentially solved to derive the analytic solution.
Sat, 01 Jan 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/237162022-01-01T00:00:00ZSolving Nonlinear Boundary Value Problems with Nonlinear Integral Boundary Conditions by Local and Nonlocal Boundary Shape Functions Methodshttp://scholars.ntou.edu.tw/handle/123456789/23717Title: Solving Nonlinear Boundary Value Problems with Nonlinear Integral Boundary Conditions by Local and Nonlocal Boundary Shape Functions Methods
Authors: Liu, Chein-Shan; Chen, Yung-Wei; Shen, Jian-Hung
Abstract: The paper considers the second-order nonlinear boundary value problem (NBVP), which is equipped with nonlinear integral boundary conditions (BCs). Two novel iterative algorithms are developed to overcome the difficulty of NBVP with double nonlinearities involved. In the first iterative algorithm, two nonlocal shape functions incorporating the linear integral terms are derived, and a nonlocal boundary shape function (NBSF) is formulated to assist the solution. Let the solution be the NBSF so that the NBVP can be exactly transformed into an initial value problem. The new variable is a free function in the NBSF, and its initial values are given. For the NBVP with linear integral BCs, three unknown constants are to be determined, while for the nonlinear integral BCs, five unknown constants are to be determined. Twopoint local shape functions and local boundary shape functions are derived for the second iterative algorithm, wherein the integral terms in the boundary conditions are viewed as unknown constants. By a few iterations, four unknown constants can be determined quickly. Through numerical experiments, these two iterative algorithms are found to be powerful for seeking quite accurate solutions. The second algorithm is slightly better than the first, with fewer iterations and a more accurate solution.
Sat, 01 Jan 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/237172022-01-01T00:00:00ZA Simplified Lindstedt-Poincare Method for Saving Computational Cost to Determine Higher Order Nonlinear Free Vibrationshttp://scholars.ntou.edu.tw/handle/123456789/20182Title: A Simplified Lindstedt-Poincare Method for Saving Computational Cost to Determine Higher Order Nonlinear Free Vibrations
Authors: Liu, Chein-Shan; Chen, Yung-Wei
Abstract: In order to improve the Lindstedt-Poincare method to raise the accuracy and the performance for the application to strongly nonlinear oscillators, a new analytic method by engaging in advance a linearization technique in the nonlinear differential equation is developed, which is realized in terms of a weight factor to decompose the nonlinear term into two sides. We expand the constant preceding the displacement in powers of the introduced parameter so that the coefficients can be determined to avoid the appearance of secular solutions. The present linearized Lindstedt-Poincare method is easily implemented to provide accurate higher order analytic solutions of nonlinear oscillators, such as Duffing and van Der Pol nonlinear oscillators. The accuracy of analytic solutions is evaluated by comparing to the numerical results obtained from the fourth-order Runge-Kotta method. The major novelty is that we can simplify the Lindstedt-Poincare method to solve strongly a nonlinear oscillator with a large vibration amplitude.
Wed, 01 Dec 2021 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/201822021-12-01T00:00:00ZThe Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffleshttp://scholars.ntou.edu.tw/handle/123456789/17300Title: The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles
Authors: Shih, Chao-Feng; Chen, Yung-Wei; Chang, Jiang-Ren; Soon, Shih-Ping
Abstract: In this paper, the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles. When considering solving sloshing problems with baffles by using boundary integral methods, degenerate geometry and problems of numerical instability are inevitable. To avoid numerical instability, the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance. Again, the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme. A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems (IBVPs) at each time step. More importantly, the parameters of the algorithm, namely, the T-complete function, dissipation factor, and time step, can obtain a linear relationship. The boundary noise interference and energy conservation are successfully overcome, and the accuracy of the boundary value problem is also improved. Finally, benchmark cases are used to verify the correctness of the numerical algorithm. The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.
Mon, 01 Nov 2021 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/173002021-11-01T00:00:00ZShip Deficiency Data of Port State Control to Identify Hidden Risk of Target Shiphttp://scholars.ntou.edu.tw/handle/123456789/19105Title: Ship Deficiency Data of Port State Control to Identify Hidden Risk of Target Ship
Authors: Shen, Jian-Hung; Liu, Chung-Ping; Chang, Ki-Yin; Chen, Yung-Wei
Abstract: In the new inspection regime (NIR) of port state control (PSC), the criteria for being judged as a standard risk ship (SRS) is too broad. Some ships are classified as SRS even though they have a large number of ship deficiencies. This paper develops a selection system to identify the hidden risk of target ships in the SRS category using PSC inspection records. This system allows the target ship to be used to help reduce cases of flags being greylisted or blacklisted, which can cause huge shipping losses. This study analyzes ship deficiency data in the Tokyo memorandum of understanding (Tokyo MoU) database. It adopts the multiple criteria decision making (MCDM) model as a data processing technique to build a risk assessment scale. It uses fuzzy importance performance analysis (F-IPA) and technology for order preference by similarity to the ideal solution (TOPSIS) for its analysis. Subsequently, the weights of F-IPA and TOPSIS are adopted into the MCDM model. This article also consulted the Tokyo MoU database. It has been verified that the next time PSC inspection, the system hits 83.3% of the hidden risk ships in the SRS category. Thus, this system will help inspectors be more insightful for target ships.</p>
Fri, 01 Oct 2021 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/191052021-10-01T00:00:00ZSolving nonlinear elliptic equations in arbitrary plane domains by using a new splitting and linearization techniquehttp://scholars.ntou.edu.tw/handle/123456789/17326Title: Solving nonlinear elliptic equations in arbitrary plane domains by using a new splitting and linearization technique
Authors: Liu, Chein-Shan; El-Zahar, Essam R.; Chen, Yung-Wei
Abstract: For solving nonlinear elliptic equations given in arbitrary plane domains, the meshless methods of radial-polynomial and Pascal-polynomial are easy to programming, which are employed as the bases to expand the solution. After a simple collocation technique, we can derive nonlinear equations to determine the expansion coefficients. We adopt a splitting parameter to split the nonlinear term into two nonlinear parts, which are separately placed on both sides of the nonlinear elliptic equation. Then, a new linearization technique is used to treat the nonlinear part on the left-hand side. In each iteration, the linear system of equations is regularized by the multiple-scale technique. The proposed methods converge very fast to obtain very accurate numerical solutions, which confirm the validity of the presented novel splitting and linearizing technique (NSLT) to solve nonlinear elliptic equations in arbitrary plane domains.
Thu, 01 Apr 2021 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/173262021-04-01T00:00:00ZCONSTRAINT-TYPE FICTITIOUS TIME INTEGRATION METHOD FOR SOLVING NON-LINEAR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONShttp://scholars.ntou.edu.tw/handle/123456789/15023Title: CONSTRAINT-TYPE FICTITIOUS TIME INTEGRATION METHOD FOR SOLVING NON-LINEAR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
Authors: Yung-Wei Chen; Chein-Shan Liu; Yen-Shen Chang; Jiang-Ren Chang
Abstract: In this paper, we propose a constraint-type fictitious time integration method (FTIM) for solving multi-dimensional non-linear elliptic-type partial differential equations. Based on the variable transformation of FTIM, the original governing equation is transformed into a new parabolic equation of an evolution type by introducing a space-time variable, and a new time integration direction is obtained. However, the space-time variable depends on the governing equation, boundary condition and fictitious time variable, especially due to the nonlinear effect. Previous studies have not discussed the definition of these nonlinear parameter problems, which may result in severe numerical instability and inaccuracy. To completely overcome this nonlinear parameter problem, a space-time variable with a minimum fictitious time size is introduced into the algorithm. By imposing a constraint condition that involves the system energy in the space domain and the minimum fictitious time step, the proposed scheme can absolutely satisfy the stringent convergence criterion and can quickly approach the true solution, even under a very small time step. More importantly, the convergence speed depends only on a space-time variable. The accuracy and efficiency of the scheme are evaluated by comparing the estimation results with those of previous studies. The obtained results demonstrate that the proposed method efficiently finds the true solution and can significantly improve both the accuracy and convergence.
Mon, 01 Jun 2020 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/150232020-06-01T00:00:00ZA Novel Transparent Microwave Thin Film Coating Technique Applied to Dual-Band Antennashttp://scholars.ntou.edu.tw/handle/123456789/13227Title: A Novel Transparent Microwave Thin Film Coating Technique Applied to Dual-Band Antennas
Authors: Lin, Y. M.; Wu, H. W.; Yung-Wei Chen; Hung, C. Y.; Chang, S. J.; Su, Y. K.
Fri, 01 Nov 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132272019-11-01T00:00:00ZSolving a nonlinear convection-diffusion equation with source and moving boundary both unknown by a family of homogenization functionshttp://scholars.ntou.edu.tw/handle/123456789/2964Title: Solving a nonlinear convection-diffusion equation with source and moving boundary both unknown by a family of homogenization functions
Authors: Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Thu, 01 Aug 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29642019-08-01T00:00:00ZIDENTIFYING NONLINEAR OSCILLATORS BY AN ENERGETIC FUNCTIONAL IN THE LINEAR SPACE OF TEMPORAL BOUNDARY FUNCTIONShttp://scholars.ntou.edu.tw/handle/123456789/2965Title: IDENTIFYING NONLINEAR OSCILLATORS BY AN ENERGETIC FUNCTIONAL IN THE LINEAR SPACE OF TEMPORAL BOUNDARY FUNCTIONS
Authors: Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Sat, 01 Jun 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29652019-06-01T00:00:00ZIDENTIFYING NONLINEAR OSCILLATORS BY AN ENERGETIC FUNCTIONAL IN THE LINEAR SPACE OF TEMPORAL BOUNDARY FUNCTIONShttp://scholars.ntou.edu.tw/handle/123456789/22430Title: IDENTIFYING NONLINEAR OSCILLATORS BY AN ENERGETIC FUNCTIONAL IN THE LINEAR SPACE OF TEMPORAL BOUNDARY FUNCTIONS
Authors: Liu, Chein-Shan; Chen, Yung-Wei; Chang, Jiang-Ren
Abstract: We resolve the inverse problems of a second-order nonlinear oscillator to recover time-dependent damping function and nonlinear restoring force, with the help of temporal boundary data measured at initial time and final time. By using these data, a sequence of temporal boundary functions of time is derived, which satisfy the measured temporal boundary conditions automatically, and are at least the fourth-order polynomials of time. All the temporal boundary functions and zero element constitute a linear space, and a new concept of energetic functional is introduced in the linear space, of which the energy is preserved for each energetic temporal boundary function. We employ the energetic temporal boundary functions as the bases of numerical solutions. Then, the linear systems are derived and the iterative algorithms used to recover the unknown nonlinear oscillators are developed from the energetic functional, which are convergent very fast. We can recover the damping functions and restoring forces of nonlinear oscillators, among them the nonlinear ship rolling oscillator and the Duffing nonlinear oscillator are of tested examples. The required data are parsimonious, merely the measured temporal boundary data of displacement and velocity, and the temporal boundary data of unknown function to be recovered.
Sat, 01 Jun 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/224302019-06-01T00:00:00ZA backward-forward Lie-group shooting method for nonhomogeneous multi-dimensional backward heat conduction problems under a long time spanhttp://scholars.ntou.edu.tw/handle/123456789/13207Title: A backward-forward Lie-group shooting method for nonhomogeneous multi-dimensional backward heat conduction problems under a long time span
Authors: Yung-Wei Chen
Mon, 01 Apr 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132072019-04-01T00:00:00ZSimultaneous determination of the heat source and the initial data by using an explicit Lie-group shooting methodhttp://scholars.ntou.edu.tw/handle/123456789/13206Title: Simultaneous determination of the heat source and the initial data by using an explicit Lie-group shooting method
Authors: Yung-Wei Chen
Mon, 01 Apr 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132062019-04-01T00:00:00ZAn Explicit/Implicit Lie-group Scheme for Solving Problems of Nonlinear Sloshing Behaviorshttp://scholars.ntou.edu.tw/handle/123456789/13214Title: An Explicit/Implicit Lie-group Scheme for Solving Problems of Nonlinear Sloshing Behaviors
Authors: Yung-Wei Chen; Shih, C. F.; Liu, Y. C.; Soon, S. P.
Fri, 01 Mar 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132142019-03-01T00:00:00ZA modified Lie-group shooting method for multi-dimensional backward heat conduction problems under long time spanhttp://scholars.ntou.edu.tw/handle/123456789/13204Title: A modified Lie-group shooting method for multi-dimensional backward heat conduction problems under long time span
Authors: Yung-Wei Chen
Sat, 01 Dec 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132042018-12-01T00:00:00ZA regularized Fourier sine series solution of a 3D backward heat conduction problem with extremal long time spanhttp://scholars.ntou.edu.tw/handle/123456789/2962Title: A regularized Fourier sine series solution of a 3D backward heat conduction problem with extremal long time span
Authors: Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Sat, 01 Dec 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29622018-12-01T00:00:00ZTHE TREFFTZ TEST FUNCTIONS METHOD FOR SOLVING THE GENERALIZED INVERSE BOUNDARY VALUE PROBLEMS OF LAPLACE EQUATIONhttp://scholars.ntou.edu.tw/handle/123456789/2963Title: THE TREFFTZ TEST FUNCTIONS METHOD FOR SOLVING THE GENERALIZED INVERSE BOUNDARY VALUE PROBLEMS OF LAPLACE EQUATION
Authors: Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Mon, 01 Oct 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29632018-10-01T00:00:00ZA highly accurate backward-forward algorithm for multi-dimensional backward heat conduction problems in fictitious time domainshttp://scholars.ntou.edu.tw/handle/123456789/13205Title: A highly accurate backward-forward algorithm for multi-dimensional backward heat conduction problems in fictitious time domains
Authors: Yung-Wei Chen
Tue, 01 May 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132052018-05-01T00:00:00ZA high-order Lie groups scheme for solving the recovery of external force in nonlinear systemhttp://scholars.ntou.edu.tw/handle/123456789/2969Title: A high-order Lie groups scheme for solving the recovery of external force in nonlinear system
Authors: Liu, Y. C.; Wang, Y. T.; Jiang-Ren Chang; Yung-Wei Chen
Mon, 01 Jan 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29692018-01-01T00:00:00ZDesign of New Eight-Channel Diplexer for Multiband Wireless Communication Systemhttp://scholars.ntou.edu.tw/handle/123456789/13215Title: Design of New Eight-Channel Diplexer for Multiband Wireless Communication System
Authors: Yung-Wei Chen; Wu, H. W.; Chiu, C. T.; Su, Y. K.
Mon, 01 Jan 2018 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132152018-01-01T00:00:00ZCOST OF SALVAGE-A COMPARATIVE FORM APPROACHhttp://scholars.ntou.edu.tw/handle/123456789/11845Title: COST OF SALVAGE-A COMPARATIVE FORM APPROACH
Authors: Chiu, C. S.; Ki-Yin Chang; Tseng, W. J.; Chung-Ping Liu; Yung-Wei Chen
Abstract: The most important principle of salvage is the “No Cure-No Pay” basis, if there is no recovery, there is no payment, whatever the expense of the operation. However, this principle has changed in recent years to reflect the public interest in prevention of damage to the environment (Mudric, 2010). The salvor can now contract in such a way that he is shielded from loss when responding to high risk or low value casualties (so called as “No Cure-Some pay”). Salvage is a high-profit business and high-risk as well in the world. The case of the Costa Concordia - by no means one of the largest cruise ships - has highlighted many things, not least that, despite technological advances, casualties will continue to happen and they can happen to mega ships. Different forms of salvage contract will result in different salvage awards. The aim of this article is to provide a methodology to measure the costs of salvage from the perspective of shipowner.
Fri, 01 Dec 2017 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/118452017-12-01T00:00:00ZDesign of Compact Six-Channel Diplexerhttp://scholars.ntou.edu.tw/handle/123456789/13216Title: Design of Compact Six-Channel Diplexer
Authors: Yung-Wei Chen; Wu, H. W.; Dai, Z. J.; Su, Y. K.
Sat, 01 Oct 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132162016-10-01T00:00:00ZHigh order implicit and explicit Lie-group schemes for solving backward heat conduction problemshttp://scholars.ntou.edu.tw/handle/123456789/13202Title: High order implicit and explicit Lie-group schemes for solving backward heat conduction problems
Authors: Yung-Wei Chen
Sat, 01 Oct 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132022016-10-01T00:00:00ZThe recovery of external force in nonlinear system by using a weak-form integral methodhttp://scholars.ntou.edu.tw/handle/123456789/2960Title: The recovery of external force in nonlinear system by using a weak-form integral method
Authors: Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Sat, 01 Oct 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29602016-10-01T00:00:00ZAPPLICATION OF A RESIDUAL-NORM-BASED ALGORITHM TO SOLVE ELLIPTIC BOUNDARY VALUE PROBLEMShttp://scholars.ntou.edu.tw/handle/123456789/2977Title: APPLICATION OF A RESIDUAL-NORM-BASED ALGORITHM TO SOLVE ELLIPTIC BOUNDARY VALUE PROBLEMS
Authors: Chang, C. M.; Hui-Ming Fang; Pai-Chen Guan; Yung-Wei Chen
Mon, 01 Aug 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29772016-08-01T00:00:00ZA multiple scale Trefftz method for the Laplace equation subjected to large noisy boundary datahttp://scholars.ntou.edu.tw/handle/123456789/13203Title: A multiple scale Trefftz method for the Laplace equation subjected to large noisy boundary data
Authors: Yung-Wei Chen
Tue, 01 Mar 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132032016-03-01T00:00:00ZNew Triple-Passband Bandpass Filter Using Multipath Stub Loaded Resonatorshttp://scholars.ntou.edu.tw/handle/123456789/13241Title: New Triple-Passband Bandpass Filter Using Multipath Stub Loaded Resonators
Authors: Wu, H. W.; Jian, L. Y.; Yung-Wei Chen; Su, Y. K.
Tue, 01 Mar 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132412016-03-01T00:00:00ZMoving Object Counting Using a Tripwire in H.265/HEVC Bitstreams for Video Surveillancehttp://scholars.ntou.edu.tw/handle/123456789/13210Title: Moving Object Counting Using a Tripwire in H.265/HEVC Bitstreams for Video Surveillance
Authors: Yung-Wei Chen; Chen, K.; Yuan, S. Y.; Kuo, S. Y.
Fri, 01 Jan 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132102016-01-01T00:00:00ZDISCUSSION ON THE MAXIMUM STORM RADIUS EQUATIONS WHEN CALCULATING TYPHOON WAVEShttp://scholars.ntou.edu.tw/handle/123456789/2976Title: DISCUSSION ON THE MAXIMUM STORM RADIUS EQUATIONS WHEN CALCULATING TYPHOON WAVES
Authors: Chang, C. M.; Hui-Ming Fang; Chuang, S. H.; Yung-Wei Chen
Thu, 01 Oct 2015 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29762015-10-01T00:00:00ZA Modified Algorithm of Steepest Descent Method for Solving Unconstraint Nonlinear Optimization Problemshttp://scholars.ntou.edu.tw/handle/123456789/15019Title: A Modified Algorithm of Steepest Descent Method for Solving Unconstraint Nonlinear Optimization Problems
Authors: Chein-Shan Liu; Jiang-Ren Chang; Yung-Wei Chen
Abstract: The steepest descent method (SDM), which can be traced back to Cauchy (1847), is the simplest gradient method for unconstrained optimization problem. The SDM is effective for well-posed and low-dimensional nonlinear optimization problems without constraints; however, for a large-dimensional system, it converges very slowly. Therefore, a modified steepest decent method (MSDM) is developed to deal with these problems. Under the MSDM framework, the original global minimization problem is transformed into a quadratic-form minimization based on the SDM and the current iterative point. Our starting point is a manifold defined in terms of the quadratic function and a fictitious time variable. Thereafter, we can derive an iterative algorithm by including a parameter in the final stage. Through a Hopf bifurcation, this parameter indeed plays a major role to switch the situation of slow convergence to a new situation that the new algorithm converges faster. Several numerical examples are examined and compared with exact solutions. It is found that the new algorithm of the MSDM has better computational efficiency and accuracy, even for a large-dimensional non-convex minimization problem of the generalized Rosenbrock function.
Sun, 01 Feb 2015 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/150192015-02-01T00:00:00ZDesign of multi-layered bandpass filter with independently controllable triple-passband responsehttp://scholars.ntou.edu.tw/handle/123456789/13217Title: Design of multi-layered bandpass filter with independently controllable triple-passband response
Authors: Yung-Wei Chen; Wu, H. W.; Su, Y. K.
Mon, 01 Dec 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132172014-12-01T00:00:00ZA RESIDUAL-NORM BASED ALGORITHM FOR SOLVING DETERMINATE/INDETERMINATE SYSTEMS OF NON-LINEAR ALGEBRAIC EQUATIONShttp://scholars.ntou.edu.tw/handle/123456789/13201Title: A RESIDUAL-NORM BASED ALGORITHM FOR SOLVING DETERMINATE/INDETERMINATE SYSTEMS OF NON-LINEAR ALGEBRAIC EQUATIONS
Authors: Yung-Wei Chen
Wed, 01 Oct 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132012014-10-01T00:00:00ZTyrosinase inhibitors and insecticidal materials produced by Burkholderia cepacia using squid pen as the sole carbon and nitrogen sourcehttp://scholars.ntou.edu.tw/handle/123456789/13221Title: Tyrosinase inhibitors and insecticidal materials produced by Burkholderia cepacia using squid pen as the sole carbon and nitrogen source
Authors: Hsu, C. H.; Nguyen, A. D.; Yung-Wei Chen; Wang, S. L.
Tue, 01 Jul 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132212014-07-01T00:00:00ZA moving-resting process with an embedded Brownian motion for animal movementshttp://scholars.ntou.edu.tw/handle/123456789/13245Title: A moving-resting process with an embedded Brownian motion for animal movements
Authors: Yan, J.; Yung-Wei Chen; Lawrence-Apfel, K.; Ortega, I. M.; Pozdnyakov, V.; Williams, S.; Meyer, T.
Tue, 01 Apr 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132452014-04-01T00:00:00ZNew Compact Triple-Passband Bandpass Filter Using Multipath-Embedded Stepped Impedance Resonatorshttp://scholars.ntou.edu.tw/handle/123456789/13238Title: New Compact Triple-Passband Bandpass Filter Using Multipath-Embedded Stepped Impedance Resonators
Authors: Wu, H. W.; Chen, G. S.; Yung-Wei Chen
Sat, 01 Mar 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132382014-03-01T00:00:00ZApplication of a modified manifold-based exponentially convergent algorithm to solve elliptic boundary-value problemshttp://scholars.ntou.edu.tw/handle/123456789/2937Title: Application of a modified manifold-based exponentially convergent algorithm to solve elliptic boundary-value problems
Authors: Chang, C. M.; Jiang-Ren Chang; Chein-Shan Liu; Yung-Wei Chen
Wed, 01 Jan 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/29372014-01-01T00:00:00ZApplication of the Multi Scaling Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forceshttp://scholars.ntou.edu.tw/handle/123456789/15016Title: Application of the Multi Scaling Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces
Authors: Yung-Wei Chen; Jiang-Ren Chang; Fu-Hsuan Hsieh; Che-Wei Chen
Wed, 01 May 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/150162013-05-01T00:00:00ZGroup Preserving Scheme for Simulating Dynamic Ship Maneuvering Behaviorshttp://scholars.ntou.edu.tw/handle/123456789/15017Title: Group Preserving Scheme for Simulating Dynamic Ship Maneuvering Behaviors
Authors: Yung-Wei Chen; Jiang-Ren Chang; Wun-Sin Jha; Juan-Chen Huang
Wed, 01 May 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/150172013-05-01T00:00:00ZApplication of the Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forceshttp://scholars.ntou.edu.tw/handle/123456789/13200Title: Application of the Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces
Authors: Yung-Wei Chen
Tue, 01 Jan 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132002013-01-01T00:00:00ZNew ultra-wideband (UWB) bandpass filter using triangle-ring multi-mode stub-loaded resonatorhttp://scholars.ntou.edu.tw/handle/123456789/13240Title: New ultra-wideband (UWB) bandpass filter using triangle-ring multi-mode stub-loaded resonator
Authors: Wu, H. W.; Yung-Wei Chen; Chen, Y. F.
Thu, 01 Nov 2012 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/132402012-11-01T00:00:00Z