This paper illustrates how GPU computing can be used to accelerate computational fluid dynamics (CFD) simulations. For sparse linear systems arising from finite volume discretization, we evaluate and optimize the performance of Conjugate Gradient (CG) routines designed for manycore accelerators and compare against an industrial CPU-based implementation. We also investigate how the recent advanc...

Consider the linear system of equations of the form Ax = b where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse and nonsymmetric and also x, b ∈ R. We refer to this system as the original system. An explicit preconditioner M for this system is an approximation of matrix A−1. In [1], Lou presented the Backward Factored INVerse or BFINV algorithm which computes the inverse factoriz...

analysis of iterative substructuring algorithms for elliptic problems in three dimensions. Least-squares mixed-nite elements for second-order elliptic problems. A least-squares approach based on a discrete minus one inner product for rst order systems. Technical report, Brookhaven National Laboratory, 1994. 4] J. H. Bramble and J. E. Pasciak. Least-squares methods for Stokes equations based on ...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

A common problem which arises in many complex applications is to solve a sequence of linear systems of the form: Akxk = bk, for k = 1, 2, .. In these applications Ak does not generally change too much from one step k to the next, as it is often the result of a continuous process (e.g. Ak can represent the discretization of some problem at time tk.) We are faced with the problem of solving each ...

We discuss an iterative method for solving large sparse systems of equations. A hybrid method is introduced which uses ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. For Schur complement approximation on coarser graphs an incomplet...

We describe and test spai_l.l, a parallel MPI implementation of the Sparse Approximate Inverse (SPAI) preconditioner. We show that SPAI can be very effective for solving a set of very large and difficult problems on a Cray T3E. The results clearly show the value of SPAI (and approximate inverse methods in general) as the viable alternative to ILU-type methods when facing very large and difficul...

I agree with Gary Comstock's conclusion that Ilu: research program at Beltsville is not morally justified. Moreover, I have no substantial disagreement with the demils of his clear, closely-reasoned argument. However, it seems to me that two aspects of Comstock's argument call for further consideration and commentary, both because of their intrinsic philosophical interest and because they are t...