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Comparison of multi-frontal and alternating direction parallel hybrid memory iGRM direct solver for non-stationary simulations

Woźniak Maciej, Bukowska Anna

Computer Science

2020

T. 21 (4)

419-439

Three-dimensional isogeometric analysis (IGA-FEM) is a modern method for simulation. The idea is to utilize B-splines or NURBS basis functions for both computational domain descriptions and engineering computations. Refined isogeometric analysis (rIGA) employs a mixture of patches of elements with B-spline basis functions and C 0 separators between them. This enables a reduction in the computational cost of direct solvers. Both IGA and rIGA come with challenging sparse matrix structures that are expensive to generate. In this paper, we show a hybrid parallelization method using hybrid-memory parallel machines. The two-level parallelization includes the partitioning of the computational mesh into sub-domains on the first level (MPI) and loop parallelization on the second level (OpenMP). We show that the hybrid parallelization of the integration reduces the contribution of this phase significantly. We compare the multi-frontal solver and alternating direction solver, including the integration and the factorization phases.

Grammar based multi-frontal solver for isogeometric analysis in 1d

Kuźnik K., Paszyński M, Calo V.

Computer Science

2013

Vol. 14 (4)

589--613

In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability.