Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring

Abstract This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure, both sequential, partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capacity to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.

[1]  John F. Abel,et al.  Adaptive substructuring techniques in elasto-plastic finite element analysis , 1985 .

[2]  Keith Johnson,et al.  Hierarchical poly tree computer architectures defined by computational multidisciplinary mechanics , 1989 .

[3]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[4]  Joseph Padovan,et al.  Hierarchical poly tree configurations for the solution of dynamically refined finite element models , 1990 .

[5]  Joseph Padovan,et al.  Multiply constrained partitioned nonlinear equation solvers , 1988 .

[6]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[7]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[8]  G. Wempner.  Discrete approximations related to nonlinear theories of solids , 1971 .

[9]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[10]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[11]  Klaus-Jürgen Bathe,et al.  Some practical procedures for the solution of nonlinear finite element equations , 1980 .

[12]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[13]  Joseph Padovan,et al.  On the convergence of block constrained nonlinear equation solvers , 1989 .

[14]  J. Z. Zhu,et al.  The finite element method , 1977 .

[15]  J. Padovan,et al.  Locally bound constrained Newton-Raphson solution algorithms , 1986 .

[16]  Joe Padovan,et al.  Multi-level hierarchical poly tree computer architectures , 1990 .

[17]  Joseph Padovan,et al.  Constrained hierarchical least square nonlinear equation solvers , 1986 .

[18]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[19]  Charbel Farhat,et al.  A parallel active column equation solver , 1988 .

[20]  M. Crisfield,et al.  A faster modified newton-raphson iteration , 1979 .

[21]  G. Roeck,et al.  Multi-level substructuring in the elasto-plastic domain , 1989 .

[22]  Joseph Padovan,et al.  Self-adaptive predictor-corrector algorithms for static nonlinear structural analysis , 1982 .

[23]  Joseph Padovan,et al.  Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms , 1982 .

[24]  Y. Fung.  Foundations of solid mechanics , 1965 .