Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

Gene Golub ; Kwok Ko

关键词: ACCELERATORS;    ALGORITHMS;    EIGENVALUES;    KERNELS;    LINEAR ACCELERATORS;    MATRICES;    PARTIAL DIFFERENTIAL EQUATIONS;    PHYSICS;    SIMULATION;    SUPERCOMPUTERS eigenvalue problem;    linear system of equations;    filter algorithm;    HSS method;   

DOI  :  10.2172/950471
RP-ID  :  DOE/ER/41177-F
PID  :  OSTI ID: 950471
Others  :  TRN: US1000768

学科分类：核物理和高能物理

美国|英语

来源: SciTech Connect

【 摘 要 】

The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.