Parallel iterative linear solvers for multistep Runge-Kutta methods
نویسندگان
چکیده
منابع مشابه
Parallel linear system solvers for Runge-Kutta methods
If the nonlinear systems arising in implicit Runge-Kutta methods like the Radau IIA methods are iterated by (modified) Newton, then we have to solve linear systems whose matrix of coefficients is of the form I A⊗hJ with A the Runge-Kutta matrix and J an approximation to the Jacobian of the righthand side function of the system of differential equations. For larger systems of differential equati...
متن کاملParallel iterated methods based on multistep Runge-Kutta methods of Radau type
This paper investigates iterated Multistep Runge-Kutta methods of Radau type as a class of explicit methods suitable for parallel implementation. Using the idea of van der Houwen and Sommeijer 18], the method is designed in such a way that the right-hand side evaluations can be computed in parallel. We use stepsize control and variable order based on iterated approximation of the solution. A co...
متن کاملStability and B-convergence properties of multistep Runge-Kutta methods
This paper continues earlier work by the same author concerning the stability and B-convergence properties of multistep Runge-Kutta methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. A series of sufficient conditions and necessary conditions for a multistep Runge-Kutta method to be algebraically stable, diagonally stable, Bor optimally B-convergent ...
متن کاملParallel Iterated Runge Kutta Methods and Applications
The iterated Runge Kutta IRK method is an iteration scheme for the numerical solu tion of initial value problems IVP of ordinary di erential equations ODEs that is based on a predictor corrector method with an Runge Kutta RK method as corrector Embed ded approximation formulae are used to control the stepsize We present di erent parallel algorithms of the IRK method on distributed memory multip...
متن کاملSimulation-Based Analysis of Parallel Runge-Kutta Solvers
We use simulation-based analysis to compare and investigate different shared-memory implementations of parallel and sequential embedded Runge-Kutta solvers for systems of ordinary differential equations. The results of the analysis help to provide a better understanding of the locality and scalability behavior of the implementations and can be used as a starting point for further optimizations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1997
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(97)00135-0