TY - BOOK ID - 18024831 TI - A parallel multilevel partition of unity method for elliptic partial differential equations. PY - 2003 SN - 3540003517 3642593259 PB - Berlin Springer DB - UniCat KW - Differential equations, Elliptic KW - Partition of unity method. KW - Numerical solutions KW - Data processing. KW - -681.3*G18 KW - 519.63 KW - Partition of unity method KW - PUM (Numerical analysis) KW - Meshfree methods (Numerical analysis) KW - 519.63 Numerical methods for solution of partial differential equations KW - Numerical methods for solution of partial differential equations KW - 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) KW - Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) KW - Elliptic differential equations KW - Elliptic partial differential equations KW - Linear elliptic differential equations KW - Differential equations, Linear KW - Differential equations, Partial KW - -Data processing KW - 681.3*G18 KW - Numerical solutions&delete& KW - Data processing KW - 681.3 *G18 KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Computer mathematics. KW - Physics. KW - Partial differential equations. KW - Applied mathematics. KW - Engineering mathematics. KW - Analysis. KW - Computational Mathematics and Numerical Analysis. KW - Numerical and Computational Physics, Simulation. KW - Partial Differential Equations. KW - Mathematical and Computational Engineering. KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Partial differential equations KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Computer mathematics KW - Electronic data processing KW - Mathematics KW - 517.1 Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:18024831 AB - The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom. ER -