Parallel Distributed Implementations of 2D Explicit Euler Solvers

Parallel Implementations of a Multidomain Explicit High-order Accurate Euler Solvers

Scalable Parallel RK Solvers for ODEs Derived by the Method of Lines

This paper describes how the specific access structure of the Brusselator equation, a typical example for ordinary differential equations (ODEs) derived by the method of lines, can be exploited to obtain scalable distributed-memory implementations of explicit Runge-Kutta (RK) solvers. These implementations need less communication and therefore achieve better speed-ups than general explicit RK i...

Semi-explicit Parareal method based on convergence acceleration technique

The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We report a derivation of the Parareal method that uses a convergence acceleration technique to improve the accuracy of the solution. Our approach uses firstly...

Combining Explicit, Recursive Blocking for Solving Triangular Sylvester-Type Matrix Equations on Distributed Memory Platforms

Parallel ScaLAPACK-style hybrid algorithms for solving the triangular continuous-time Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel high-performance library RECSY are presented. We compare our new hybrid algorithms with parallel implementations based on the SYCT solver DTRSYL from LAPACK. Experiments show that the RECSY solvers can significantly impro...

Combining Explicit and Recursive Blocking for Solving Triangular Sylvester-Type Matrix Equations on Distributed Memory Platforms

Parallel ScaLAPACK-style hybrid algorithms for solving the triangular continuous-time Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel high-performance library RECSY are presented. We compare our new hybrid algorithms with parallel implementations based on the SYCT solver DTRSYL from LAPACK. Experiments show that the RECSY solvers can significantly impro...