Showing papers by "Paul Fischer published in 2000"
01 Jan 2000
TL;DR: In this paper, a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure was developed, and a coarse grid projection operator whose solution was computed via a fast parallel direct solver.
Abstract: As the sound speed is infinite for incompressible flows, computation of the pressure constitutes the stiffest component in the time advancement of unsteady simulations. For complex geometries, efficient solution is dependent upon the availability of fast solvers for sparse linear systems. In this paper we develop a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure. These local subdomain problems are derived from tensor products of one-dimensional finite element discretizations and admit use of fast diagonalization methods based upon matrix-matrix products. In addition, we use a coarse grid projection operator whose solution is computed via a fast parallel direct solver. The combination of overlapping Schwarz preconditioning and fast coarse grid solver provides as much as a fourfold reduction in simulation time over previously employed methods based upon deflation for parallel solution of multi-million grid point flow problems.
65 citations
TL;DR: Navier-Stokes simulations of three-dimensional flow and augmented convection in a channel with symmetric, transverse grooves on two opposite walls were performed for 180 ≤Re≤ 1600 using the spectral element technique as mentioned in this paper.
Abstract: Navier-Stokes simulations of three-dimensional flow and augmented convection in a channel with symmetric, transverse grooves on two opposite walls were performed for 180 ≤Re≤ 1600 using the spectral element technique. A series of flow transitions was observed as the Reynolds number was increased, from steady two-dimensional flow, to traveling two and three-dimensional wave structures, and finally to three-dimensional mixing
40 citations
23 Jul 2000
TL;DR: In this article, an automated method is described for creating a computational fluid dynamic (CFD) mesh of a blood vessel lumen geometry based on in vivo measurements taken by magnetic resonance (MR) imaging.
Abstract: An automated method is described for creating a computational fluid dynamic (CFD) mesh of a blood vessel lumen geometry based on in vivo measurements taken by magnetic resonance (MR) imaging. Study of the specific geometry and flow conditions in patients with vascular disease may contribute to one's understanding of the relationship between their hemodynamic environment and conditions that lead to the development and progression of arterial disease.
13 citations
01 Jan 2000
TL;DR: An automated method is described for creating a computational fluid dynamic (CFD) mesh of a blood vessel lumen geometry based on in vivo measurements taken by magnetic resonance imaging.
Abstract: An automated method is described for creating a computational fluid dynamic (CFD) mesh of a blood vessel lumen geometry based on in vivo measurements taken by magnetic resonance (MR) imaging. Study of the specific geometry and flow conditions in patients with vascular disease may contribute to one's understanding of the relationship between their hemodynamic environment and conditions that lead to the development and progression of arterial disease.
13 citations
TL;DR: This modified conjugate gradient procedure for solving A in which the approximation space is based upon the Krylov space associated with A1/p and $$\underline b $$ , for any integer p, may still be successfully applied to a variety of small, “almost-SPD” problems, and can be used to jump-start the conjugates method.
Abstract: We consider the modified conjugate gradient procedure for solving A\underline{x}e\underline{b} in which the approximation space is based upon the Krylov space associated with A1/p and \underline{b}, for any integer p. For the square-root MCG (pe2) we establish a sharpened bound for the error at each iteration via Chebyshev polynomials in \sqrt{A}. We discuss the implications of the quickly accumulating effect of an error in \sqrt{A}e\underline{b} in the initial stage, and find an error bound even in the presence of such accumulating errors. Although this accumulation of errors may limit the usefulness of this method when \sqrt{A}e\underline{b} is unknown, it may still be successfully applied to a variety of small, “almost-SPD” problems, and can be used to jump-start the conjugate gradient method. Finally, we verify these theoretical results with numerical tests.