A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the...Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the structural dynamics in multi-scale both the space domain and time domain.The discrete FEA model is partitioned into explicit and implicit parts using the nodal partition method.Multiple boundary node method is adopted to handle the interface coupled problem.In coupled region,the implicit Newmark coupled with an explicit predictor corrector Newmark whose predictive wave propagates into the implicit mesh.During the explicit subcycling process,the variables of boundary nodes are solved directly by dynamics equilibrium equation.The dissipation energy is dynamically determined in accordance with the energy balance checking.A cantilever beam and a building two numerical examples are proposed to verify that the method can greatly reduce the computing time while maintaining a high accuracy.展开更多
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ...The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.展开更多
Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain i...Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straightline interface(SI) . By using the Leray-Schauder fixed-point theorem and the discrete energy method,it is shown that the resulting CEIDD-SI algorithm is uniquely solvable,unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage,a composite interface(CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable,stable and convergent. Numerical experiments are presented to support the theoretical results.展开更多
In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic id...In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx explicitly.We give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order schemes.The optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
基金supported by the National Key Research and Development Program of China(2016YFB0201800)the National Natural Science Foundation of China(No.51475287 and No.11772192).
文摘Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the structural dynamics in multi-scale both the space domain and time domain.The discrete FEA model is partitioned into explicit and implicit parts using the nodal partition method.Multiple boundary node method is adopted to handle the interface coupled problem.In coupled region,the implicit Newmark coupled with an explicit predictor corrector Newmark whose predictive wave propagates into the implicit mesh.During the explicit subcycling process,the variables of boundary nodes are solved directly by dynamics equilibrium equation.The dissipation energy is dynamically determined in accordance with the energy balance checking.A cantilever beam and a building two numerical examples are proposed to verify that the method can greatly reduce the computing time while maintaining a high accuracy.
基金the National Natural Science Foundation of China(No.10571017)supported in part by the National Natural Science Foundation of China(No.60533020)supported in part by NSF DMS 0712744
文摘The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.
基金supported by National Natural Science Foundation of China (Grant No. 10871044)
文摘Corrected explicit-implicit domain decomposition(CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straightline interface(SI) . By using the Leray-Schauder fixed-point theorem and the discrete energy method,it is shown that the resulting CEIDD-SI algorithm is uniquely solvable,unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage,a composite interface(CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable,stable and convergent. Numerical experiments are presented to support the theoretical results.
基金supported by National Natural Science Foundation of China(Grant Nos.11601241,11671199,11571290 and 11672082)Natural Science Foundation of Jiangsu Province(Grant No.BK20160877)+1 种基金ARO(Grant No.W911NF-15-1-0226)National Science Foundation of USA(Grant No.DMS-1719410)
文摘In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx explicitly.We give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order schemes.The optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations.
