POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Architecture-cognizant divide and conquer algorithms
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Memory characteristics of iterative methods
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Journal of Parallel and Distributed Computing
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Automatically Tuned Linear Algebra Software
Automatically Tuned Linear Algebra Software
Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines
Scientific Programming
Pipelining for Locality Improvement in RK Methods
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Performance optimization of RK methods using block-based pipelining
Performance analysis and grid computing
Simulation-based analysis of parallel runge-kutta solvers
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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Runge-Kutta methods are popular methods for the solution of systems of ordinary differential equations and are provided by many scientific libraries. The performance of Runge-Kutta methods does not only depend on the specific application problem to be solved but also on the characteristics of the target machine. For processors with memory hierarchy, the locality of data referencing pattern has a large impact on the efficiency of a program. In this paper, we describe program transformations for Runge-Kutta methods resulting in programs with improved locality behavior. The transformations are based on properties of the solution method but are independent from the specific application problem or the specific target machine, so that the resulting implementation is suitable as library function. We show that the locality improvement leads to performance gains on different target machines. We also demonstrate how the locality of memory references can be further increased by exploiting the dependence structure of the right hand side function of specific ordinary differential equations.