A domainbased multilevel block ilut preconditioner for general sparse matrices. A gridbased multilevel incomplete lu factorization preconditioning technique for general sparse matrices article in applied mathematics and computation 1241. The fortran interface requires a fortran compiler, and the algebraic multigrid preconditioner requires a fortran 90 compiler. Developer reference for intel math kernel library fortran. We have used some fortran subroutines from the sparskit package to read such a format and convert it to csc and csr formats. The coefficient matrix is naturally stored in a band format. Preconditioners so far in this package include 1 iluk ilu preconditioner.
International journal of antennas and propagation hindawi. Research article pfft accelerated efie with a novel diagonal perturbed ilut preconditioner for electromagnetic scattering by conducting objects in half space. All types in this documentation refer to the standard fortran types, integer, and double precision. Bilum is portable on most unix systems that have a fortran 77 compiler. Sand for preparing in complete factorization preconditioner for positive definite matrices being neither. Ilu0 and ilut preconditioners interface description dcsrilu0 dcsrilut.
Abstractwe present a modification of the ilut algorithm due to y. Preconditioners based on incomplete lu factorization. A software package of multilevel block ilu preconditioning techniques for solving. For krylov subspace matrix iterations, this is preconditioning. Preconditioning, linear systems and matrices researchgate, the professional. The precorrected fast fourier transform pfft is first extended to a half space for general threedimensional scattering problems. A gridbased multilevel incomplete lu factorization. In this section the fortran style notations are used. Preconditioners, or accelerators are used to accelerate an iterative solution process. Thus, in the first level the matrix is permuted into a block form using block independent set ordering and an ilut factorization for the reordered. This makes it possible to use bpkit from an iterative solver written in fortran 77. I am trying to use the fgmres with ilut preconditioner for solving the penta diagonal matrix axb.
Direct iterative preconditioning for nonsymmetric linear systems. This preconditioner combines a high accuracy incomplete lu factorization with an algebraic multilevel recursive reduction. For more complete information about compiler optimizations, see our optimization. Ilut preconditioner based on the incomplete lu factorization with a threshold of a sparse matrix. Typically, a preconditioner is needed to achieve acceptable convergence of a krylov. Sparse approximate inverse methods student theses faculty of. For more complete information about compiler optimizations, see our optimization notice. Standard preconditioning techniques based on incomplete lu ilu factorizations offer a limited degree of parallelism, in general.
Although the terms preconditioner and accelerator are synonyms, hereafter only preconditioner is used. Download table operations required by iterative methods. The distinctive feature of the ilut algorithm is that it calculates each element of the preconditioner and saves each one if it satisfies two conditions simultaneously. Restarted gm res and bicgstab, with and without the ilut preconditioner, were tested on several wellknown. For the ilu0 preconditioner, the total memory required was 125 mb. In this package, there is also a fortran subroutine to compute the ilut preconditioner. A few of the alternatives advocated so far consist of either using some form of polynomial preconditioning or applying the usual ilu factorization to a matrix obtained from a multicolor ordering. Sparskit is a general purpose fortran77 library for sparse matrix computations. Research article pfft accelerated efie with a novel. The concepts required to understand the use of the intel mkl preconditioner routines are discussed in the linear solvers basics. This scheme is based on the electric field integral equation efie with a halfspace greens function. A highly efficient and robust scheme is proposed for analyzing electromagnetic scattering from electrically large arbitrary shaped conductors in a half space. Amg method and, although it can be used as a blackbox preconditioner, it o.
Sparskit is a general purpose fortran77 library for sparse matrix. Suppose that the set p contains a bunch of artificial linear systems. Preconditioning techniques for large linear systems. Sparse approximate inverse, preconditioning, krylov subspace methods. In each program, we used the overlay technique within fortran 8. A block version of leftlooking ainv preconditioner with. This paper describes a domainbased multilevel block ilu preconditioner bilutm for solving general sparse linear systems. Ilu0 and ilut preconditioners interface description. Intel mkl pardiso parallel direct sparse solver interface intel.
This setting is effective for both iluk and ilut factorization. Note that exactly the same preconditioner can be obtained from ilut by setting the drop. Preconditioners based on incomplete lu factorization technique. In some cases, their use can reduce the number of iterations dramatically and thus lead to better solver performance. Multilevel block ilu preconditioning techniques for.
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