Parallel-Sparse Symmetrical/Unsymmetrical Finite Element Domain Decomposition Solver with Multi-Point Constraints for Structural/Acoustic Analysis

Details of parallel-sparse Domain Decomposition (DD) with multi-point constraints (MPC) formulation are explained. Major computational components of the DD formulation are identified. Critical roles of parallel (direct) sparse and iterative solvers with MPC are discussed within the framework of DD formulation. Both symmetrical and unsymmetrical system of simultaneous linear equations (SLE) can be handled by the developed DD formulation. For symmetrical SLE, option for imposing MPC equations is also provided. Large-scale (up to 25 million unknowns involving complex numbers) structural and acoustic Finite Element (FE) analysis are used to evaluate the parallel computational performance of the proposed DD implementation using different parallel computer platforms. Numerical examples show that the authors’ MPI/FORTRAN code is significantly faster than the commercial parallel sparse solver. Furthermore, the developed software can also conveniently and efficiently solve large SLE with MPCs, a feature not available in almost all commercial parallel sparse solvers. Key-Words: Domain Decomposition Solver, Multi-Point Constraints, Parallel Computation, Symmetrical/Unsymmetrical Simultaneous Linear Equation, Finite Element Analysis, Acoustic/Structural Engineering Applications, Iterative Algorithms, Sparse Assembly, Sparse Factorization. WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS Siroj Tungkahotara, Willie R. Watson, Duc T. Nguyen, Subramaniam D. Rajan ISSN: 1991-8747 37 Issue 1, Volume 6, January 2011 1 Finite Element Analysis With Domain Decomposition (DD) Formulations The finite element equilibrium equation (state equation) in terms of displacements, is given in [1][6] = K z s (1) where s = vector of effective nodal loads on the structure z = state variable vector of (e.g. nodal displacements) K = global stiffness matrix, with dimension NxN Using the DD concept, Eq. (1) can be re-written (in the partitioned form) as