A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis
SIAM Journal on Matrix Analysis and Applications
Parallel Computing - Parallel matrix algorithms and applications
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This paper describes the implementation of parallel computing to model seismic waves in heterogeneous media based on Laguerre transform with respect to time. The main advantages of the transform are a definite sign of the spatial part of the operator and its independence of the parameter of separation. This property allows one to efficiently organize parallel computations by means of decomposition of the computational domain with successive application of the additive Schwarz method. At each step of the Schwarz alternations, a system of linear algebraic equations in each subdomain is resolved independently of all the others. A proper choice of Domain Decomposition reduces the size of matrices and ensures the use of direct solvers, in particular, the ones based on LU decomposition. Thanks to the independence of the matrix of the parameter of Laguerre transform with respect to time, LU decomposition for each subdomain is done only once, saved in the memory and used afterwards for different right-hand sides. A software is being developed for a cluster using hybrid OpenMP and MPI parallelization. At each cluster node, a system of linear algebraic equations with different right-hand sides is solved by the direct sparse solver PARDISO from Intel Math Kernel Library (Intel MKL). The solver is extensively parallelized and optimized for the high performance on many core systems with shared memory. A high performance parallel algorithm to solve the problem has been developed. The algorithm scalability and efficiency is investigated. For a two-dimensional heterogeneous medium, describing a realistic geological structure, which is typical of the North Sea, the results of numerical modeling are presented.