Experiences with sparse matrix solvers in parallel ODE software
For solving a stiff initial value problem, one of the most powerful methods is an implicit Runge-Kutta (RK) scheme. However, in such a method, since one has to solve a system of nonlinear equations of dimension \(sd\) in every time step, where \(s\) is the number of stages, this may require a lot of computational effort. On parallel computer architectures, the costs can be reduced significantly. In this paper, the authors focus on parallel software for ordinary differential equations (PSODE). PSODE is an implementation of a Radau IIA method with a Newton-type iteration process, which reduces the nonlinear systems to sequences of linear systems. For problems arising in practice it often occurs that the components of the derivative function only depend on a small number of variables. Such problems lead to linear systems of which the matrix is sparse. The goal of this paper is to reduce the linear algebra costs for such problems by using a sparse matrix solver like MA28 and Y12M. The numerical results presented give insight into the behaviour of these matrix solvers.
parallel software for ordinary differential equations
scientific article; zbMATH DE number 915123