The purpose of this paper is to present a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two-and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients. The discrete equations are assumed to be defined on a logically rectangular grid, obtained possibly through grid generation for a problem defined on an irregular domain. The basic algorithm is described along with some modifications which are designed to improve its efficiency and robustness for certain types of problem cases. FORTRAN codes that implement the two-and three-dimensional semicoarsening multigrid algorithms are described briefly, and numerical results are presented.
No abstract
Several viral transport experiments were conducted in a model aquifer 1 m long, using bacteriophages MS2 and phiX174 at various pH (4.6 to 8.3) conditions, to increase our understanding of virus behavior in ground water. The results indicate the existence of a critical pH at which the virus behavior changes abruptly. This is supported by data from field and batch experiments. The critical pH is determined to be 0.5 unit below the highest isoelectric point of the virus and porous medium. When water pH is below the critical pH, the virus has an opposite charge to at least one component of the porous medium, and is almost completely and irreversibly removed from the water. This suggests that electrostatic attraction at a subcritical water pH condition is an important factor controlling virus attenuation in ground water. The concept of critical pH can assist in the design of geologic barriers for preventing viral contamination in ground water.
Abstract. This paper is concerned with the treatment of higher order multi-grid techniques for obtaining accurate finite difference approximations to partial differential equations. The three basic techniques considered are a multi-grid process involving smoothing via higher order difference approximations, iterated defect corrections with multi-grid used as an inner loop equation solver, and tau-extrapolation. Efficient versions of each of these three basic schemes are developed and analyzed by local mode analysis and numerical experiments. The numerical tests focus on fourth and sixth order discretizations of Poisson's equations and demonstrate that the three methods performed similarly yet substantially better than the usual multi-grid method, even when the right-hand side lacked sufficient smoothness.Introduction. The goal of the numerical solution of partial differential equations is to obtain the highest accuracy possible within the constraints imposed by limitations in computer time and storage. Using higher order discretizations of the differential equation provides a means of obtaining this accuracy without requiring large amounts of storage. Higher order approximations, however, are more expensive to obtain due to the added complexity of the resulting discretized equations. Recent advances in fast solution techniques have made it more feasible to attempt these super accurate approximations. The Multi-Grid method is one such fast solver which is easily adapted to accommodate higher order processes. This paper treats three higher order multi-grid methods applied to finite difference discretizations of a linear partial differential equation.This paper is primarily concerned with comparing the numerical performance of the three higher order multi-grid solution processes. The model problem used for the
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