کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
522496 867830 2010 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A parallel additive Schwarz preconditioned Jacobi–Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A parallel additive Schwarz preconditioned Jacobi–Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation
چکیده انگلیسی

We develop a parallel Jacobi–Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi–Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc’s efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schrödinger’s equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi–Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0 GHz processors.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 229, Issue 8, 20 April 2010, Pages 2932–2947
نویسندگان
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