The Experts below are selected from a list of 9270 Experts worldwide ranked by ideXlab platform
Arezou Ghesmati - One of the best experts on this subject based on the ideXlab platform.
-
application of the dual reciprocity boundary integral equation technique to solve the nonlinear klein gordon equation
Computer Physics Communications, 2010Co-Authors: Mehdi Dehghan, Arezou GhesmatiAbstract:This paper aims to obtain approximate solutions of the Nonlinear Klein–Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor–corrector Scheme to the nonlinearity which appears in the problem. We employ the time Stepping Scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated. © 2010 Elsevier B.V. All rights reserved.
-
solution of the second order one dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation drbie method
Engineering Analysis With Boundary Elements, 2010Co-Authors: Mehdi Dehghan, Arezou GhesmatiAbstract:In this paper, we use a numerical method based on the boundary integral equation (BIE) and an application of the dual reciprocity method (DRM) to solve the second-order one space-dimensional hyperbolic telegraph equation. Also the time Stepping Scheme is employed to deal with the time derivative. In this study, we have used three different types of radial basis functions (cubic, thin plate spline and linear RBFs), to approximate functions in the dual reciprocity method (DRM). To confirm the accuracy of the new approach and to show the performance of each of the RBFs, several examples are presented. The convergence of the DRBIE method is studied numerically by comparison with the exact solutions of the problems.
Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.
-
the dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations
Mathematical Methods in The Applied Sciences, 2016Co-Authors: Mehdi Dehghan, Mansour SafarpoorAbstract:In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time-fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time-Stepping Scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector Scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.
-
application of the dual reciprocity boundary integral equation technique to solve the nonlinear klein gordon equation
Computer Physics Communications, 2010Co-Authors: Mehdi Dehghan, Arezou GhesmatiAbstract:This paper aims to obtain approximate solutions of the Nonlinear Klein–Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor–corrector Scheme to the nonlinearity which appears in the problem. We employ the time Stepping Scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated. © 2010 Elsevier B.V. All rights reserved.
-
solution of the second order one dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation drbie method
Engineering Analysis With Boundary Elements, 2010Co-Authors: Mehdi Dehghan, Arezou GhesmatiAbstract:In this paper, we use a numerical method based on the boundary integral equation (BIE) and an application of the dual reciprocity method (DRM) to solve the second-order one space-dimensional hyperbolic telegraph equation. Also the time Stepping Scheme is employed to deal with the time derivative. In this study, we have used three different types of radial basis functions (cubic, thin plate spline and linear RBFs), to approximate functions in the dual reciprocity method (DRM). To confirm the accuracy of the new approach and to show the performance of each of the RBFs, several examples are presented. The convergence of the DRBIE method is studied numerically by comparison with the exact solutions of the problems.
Kenneth G. Powell - One of the best experts on this subject based on the ideXlab platform.
-
a parallel explicit implicit time Stepping Scheme on block adaptive grids
Journal of Computational Physics, 2006Co-Authors: G Toth, T I Gombosi, Darren L De Zeeuw, Kenneth G. PowellAbstract:We present a parallel explicit/implicit time integration Scheme well suited for block-adaptive grids. The basic idea of the algorithm is that the time Stepping Scheme can differ in the blocks of the grid for a given time step: an explicit Scheme is used in the blocks where the local stability requirement is not violated and an implicit Scheme is used in the blocks where the explicit Scheme would be unstable. The implicit Scheme is second order in time. The non-linear system of equations is linearized with Newton linearization. The linear system is solved with a preconditioned Krylov subspace iterative Scheme. The Schwarz type preconditioning is also based on the block structure of the grid. We discuss load balancing for parallel execution and the optimal choice of the time step for speed and robustness. The parallel efficiency of the Scheme is demonstrated for the equations of magnetohydrodynamics with a geophysics application in three dimensions. The control of the numerical divergence of the magnetic field in combination with the explicit/implicit time Stepping Scheme is also discussed.
-
regular article a solution adaptive upwind Scheme for ideal magnetohydrodynamics
Journal of Computational Physics, 1999Co-Authors: Kenneth G. Powell, T I Gombosi, Philip L. Roe, Timur Linde, Darren L De ZeeuwAbstract:This paper presents a computational Scheme for compressible magnetohydrodynamics (MHD). The Scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-Stepping Scheme; and solution-adaptive refinement and coarsening. In addition, a method for increasing the accuracy of the Scheme by subtracting off an embedded steady magnetic field is presented. Each of the pieces of the Scheme is described, and the Scheme is validated and its accuracy assessed by comparison with exact solutions. Results are presented for two three-dimensional calculations representative of the interaction of the solar wind with a magenetized planet.
-
regular article a solution adaptive upwind Scheme for ideal magnetohydrodynamics
Journal of Computational Physics, 1999Co-Authors: Kenneth G. Powell, T I Gombosi, Timur Linde, Darren L De ZeeuwAbstract:This paper presents a computational Scheme for compressible magnetohydrodynamics (MHD). The Scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-Stepping Scheme; and solution-adaptive refinement and coarsening. In addition, a method for increasing the accuracy of the Scheme by subtracting off an embedded steady magnetic field is presented. Each of the pieces of the Scheme is described, and the Scheme is validated and its accuracy assessed by comparison with exact solutions. Results are presented for two three-dimensional calculations representative of the interaction of the solar wind with a magenetized planet.
David E Stewart - One of the best experts on this subject based on the ideXlab platform.
-
an implicit time Stepping Scheme for rigid body dynamics with coulomb friction
International Conference on Robotics and Automation, 2000Co-Authors: David E Stewart, Jeff TrinkleAbstract:In this paper a new time-Stepping method for simulating systems of rigid bodies is given. Unlike methods which take an instantaneous point of view, our method is based on impulse-momentum equations, and so does not need to explicitly resolve impulsive forces. On the other hand, our method is distinct from previous impulsive methods in that it does not require explicit collision checking and it can handle simultaneous impacts. Numerical results are given for one planar and one three dimensional example, which demonstrate the practicality of the method, and its convergence as the step size becomes small.
-
convergence of a time Stepping Scheme for rigid body dynamics and resolution of painleve s problem
Archive for Rational Mechanics and Analysis, 1998Co-Authors: David E StewartAbstract:This paper gives convergence theory for a new implicit time‐Stepping Scheme for general rigid‐body dynamics with Coulomb friction and purely inelastic collisions and shocks. An important consequence of this work is the proof of existence of solutions of rigid‐body problems which include the famous counterexamples of Painleve. The mathematical basis for this work is the formulation of the rigid‐body problem in terms of measure differential inclusions of Moreau and Monteiro Marques. The implicit time‐Stepping method is based on complementarity problems, and is essentially a particular case of the algorithm described in Anitescu & Potra [2], which in turn is based on the formulation in Stewart & Trinkle [47].
-
an implicit time Stepping Scheme for rigid body dynamics with inelastic collisions and coulomb friction
International Journal for Numerical Methods in Engineering, 1996Co-Authors: David E Stewart, Jeff TrinkleAbstract:In this paper a new time-Stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro-Marques, except that the numerical formulation used here ensures that there is no inter-penetration of rigid bodies, unlike their velocity-based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three-dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.
Jeff Trinkle - One of the best experts on this subject based on the ideXlab platform.
-
an implicit time Stepping Scheme for rigid body dynamics with coulomb friction
International Conference on Robotics and Automation, 2000Co-Authors: David E Stewart, Jeff TrinkleAbstract:In this paper a new time-Stepping method for simulating systems of rigid bodies is given. Unlike methods which take an instantaneous point of view, our method is based on impulse-momentum equations, and so does not need to explicitly resolve impulsive forces. On the other hand, our method is distinct from previous impulsive methods in that it does not require explicit collision checking and it can handle simultaneous impacts. Numerical results are given for one planar and one three dimensional example, which demonstrate the practicality of the method, and its convergence as the step size becomes small.
-
an implicit time Stepping Scheme for rigid body dynamics with inelastic collisions and coulomb friction
International Journal for Numerical Methods in Engineering, 1996Co-Authors: David E Stewart, Jeff TrinkleAbstract:In this paper a new time-Stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro-Marques, except that the numerical formulation used here ensures that there is no inter-penetration of rigid bodies, unlike their velocity-based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three-dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.
