Two and a half thousand years ago the ancient atomists made a suggestion that space has a cellular structure, is material and consists of elementary cells. In 1900 Plank found the elementary length L*=10-33 cm. This n...Two and a half thousand years ago the ancient atomists made a suggestion that space has a cellular structure, is material and consists of elementary cells. In 1900 Plank found the elementary length L*=10-33 cm. This notion has been widely used in modern physics ever since. The properties of granular space are studied in this article on the assumption that a three-dimensional material cell with the size of Planck’s elementary length is the only material for the construction of the whole Universe. This approach allows one to account for such mysterious phenomena as inertia, ultimate velocity of transfer of material body interactions and huge difference between gravitational and Coulomb forces - the so called “Large Numbers Problem”, as well essence of electric charge and Pauli exclusions principle.展开更多
In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schu...In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.展开更多
文摘Two and a half thousand years ago the ancient atomists made a suggestion that space has a cellular structure, is material and consists of elementary cells. In 1900 Plank found the elementary length L*=10-33 cm. This notion has been widely used in modern physics ever since. The properties of granular space are studied in this article on the assumption that a three-dimensional material cell with the size of Planck’s elementary length is the only material for the construction of the whole Universe. This approach allows one to account for such mysterious phenomena as inertia, ultimate velocity of transfer of material body interactions and huge difference between gravitational and Coulomb forces - the so called “Large Numbers Problem”, as well essence of electric charge and Pauli exclusions principle.
基金developed in the framework of the associated team PhyLeas(Study of parallel hybrid sparse linear solvers) funded by INRIA where the partners are INRIA,T.U.Brunswick and University of Minnesotasupported by the US Department of Energy under grant DE-FG-08ER25841 and by the Minnesota Supercomputer Institute.
文摘In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.
