solving a large sparse set of linear equations is of the problems widely seen in every numerical investigation in the entire range of engineering disciplines. employing a finite element approach in solving partial derivative equations, the resulting stiffness matrices would contain many zero-valued elements. moreover, storing all these sparse matrices in a computer memory would slower the compu...

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fas...

This paper presents a static load balancing scheme for a parallel PDE solver targeting heterogeneous computing clusters. The proposed scheme adopts a mathematical programming approach and optimizes the execution time of the PDE solver, considering both computation and communication time. While traditional task graph scheduling algorithms only distribute loads to processors, the proposed scheme ...

Abstract A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by using a variety solvers. scalability analysis performed both direct and preconditioned iterative solvers four different pancakes with varying number turns mesh elements. It found that even two extremely time scales in system an solver com...

In this article we introduce a fast iterative solver for sparse matrices arising from the finite element discretization of elliptic PDEs. The solver uses a fast direct multi-frontal solver as a preconditioner to a simple fixed point iterative scheme. This approach combines the advantages of direct and iterative schemes to arrive at a fast, robust and accurate solver. We will show that this solv...

The traditional performance measurement for computers on scienti c application has been the Linpack benchmark [2], which evaluates the e ciency with which a machine can solve a dense system of equations. Since this operation allows for considerable reuse of data, it is possible to show performance gures a sizeable percentage of peak performance, even for machines with a severe unbalance between...

In scientific computing, several benchmarks exist that give a user some idea of the to-be-expected performance given a code and a specific computer. One widely accepted performance measurement is the Linpack benchmark [4], which evaluates the efficiency with which a machine can solve a dense system of equations. Since this operation allows for considerable reuse of data, it is possible to show ...