Parallel algorithms for successive convolution. (English) Zbl 1458.65122
The authors of the work under review, propose hybrid parallel algorithms that can handle a wide class of linear as well as nonlinear partial differential equations. In order to enable parallel simulations on distributed systems, a set of conditions that use available wave speed, either in conjunction with, or without diffusivity information, together with the size of the sub-domains (to limit the communication through an adjustment of the time step), is derived. In this frame work, boundary conditions are enforced across sub-domains in the decomposition. Results presented for two-dimensional examples consisting of linear advection, linear diffusion, and a nonlinear Hamilton-Jacobi equation, exhibit the adaptability of the methods in addressing qualitatively different partial differential equations.
Reviewer: Kanakadurga Sivakumar (Chennai)
MSC:
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 65R20 | Numerical methods for integral equations |
Keywords:
high-performance computing; domain decomposition; method-of-lines-transpose; integral solution; fast algorithms; numerical analysisReferences:
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