Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
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
Optimizing locality for ODE solvers
ICS '01 Proceedings of the 15th international conference on Supercomputing
Automatically Tuned Linear Algebra Software
Automatically Tuned Linear Algebra Software
Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines
Scientific Programming
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We consider embedded Runge-Kutta (RK) methods for the solution of ordinary differential equations (ODEs) arising from space discretizations of partial differential equations and study their efficient implementation on modern microprocessors with memory hierarchies. For those systems of ODEs, we present a block oriented pipelining approach with diagonal sweeps over the stage and approximation vector computations of RK methods. Comparisons with other efficient implementations show that this pipelining technique improves the locality behavior considerably. Runtime experiments are performed with the DOPRI5 method.