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Mathematics: Recent submissions
Now showing items 321-340 of 462
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A simple adaptive grid method in two dimensions
(Society for Industrial and Applied Mathematics, 1994-07-01)This paper gives an interpretation of the concept of equidistribution in the context of adaptive grid generation for multidimensional problems. It is shown that the equidistribution principle cannot be satisfied throughout ... -
Moving mesh partial differential equations (MMPDEs) based upon the equidistribution principle
(Society for Industrial and Applied Mathematics, 1994-06-01)This paper considers several moving mesh partial differential equations that are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh equations that have been ... -
Moving Mesh Methods for Problems with Blow-Up
(Society for Industrial and Applied Mathematics, 1996-03-01)In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the ... -
Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems
(Society for Industrial and Applied Mathematics, 1996-12-01)A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral ... -
The adaptive Verlet method
(Society for Industrial and Applied Mathematics, 1997-01-01)We discuss the integration of autonomous Hamiltonian systems via dynamical rescaling of the vector field (reparameterization of time). Appropriate rescalings (e.g., based on normalization of the vector field or on minimum ... -
Analysis of moving mesh partial differential equations with spatial smoothing
(Society for Industrial and Applied Mathematics, 1997-06-01)Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury ... -
Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity
(Society for Industrial and Applied Mathematics, 1998-07-01)The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite ... -
Moving mesh strategy based upon a gradient flow equation for two dimensional problems
(Society for Industrial and Applied Mathematics, 1999-07-01)In this paper we introduce a moving mesh method for solving PDEs in two dimensions. It can be viewed as a higher-dimensional generalization of the moving mesh PDE (MMPDE) strategy developed in our previous work for ... -
A study of monitor functions for two dimensional adaptive mesh generation
(Society for Industrial and Applied Mathematics, 1999-11-01)In this paper we study the problem of two-dimensional adaptive mesh generation using a variational approach and, specifically, the effect that the monitor function has on the resulting mesh behavior. The basic theoretical ... -
A Moving Mesh Method Based on the Geometric Conservation Law
(Society for Industrial and Applied Mathematics, 2002-01-01)A new adaptive mesh movement strategy is presented, which, unlike many existing moving mesh methods, targets the mesh velocities rather than the mesh coordinates. The mesh velocities are determined in a least squares ... -
Variational Mesh Adaptation Methods for Axisymmetrical Problems
(Society for Industrial and Applied Mathematics, 2003-01-01)We study variational mesh adaptation for axially symmetric solutions to two-dimensional problems. The study is focused on the relationship between the mesh density distribution and the monitor function and is carried out ... -
Convergence analysis of pseudospectral collocation methods for a singular differential equation
(Society for Industrial and Applied Mathematics, 2003-01-02)Solutions of partial differential equations with coordinate singularities often have special behavior near the singularities, which forces them to be smooth. Special treatment for these coordinate singularities is necessary ... -
Measuring mesh qualities and application to variational mesh adaptation
(Society for Industrial and Applied Mathematics, 2005-11-01)The mesh assessment problem is investigated in this paper by taking into account the shape and size of elements and the solution behavior. Three elementwise mesh quality measures characterizing the shape, alignment, and ... -
A moving mesh WENO method for one-dimensional conservation laws
(Society for Industrial and Applied Mathematics, 2012-10-01)In this paper, we develop an efficient moving mesh weighted essentially nonoscillatory (WENO) method for one-dimensional hyperbolic conservation laws. The method is based on the quasi-Lagrange approach of the moving mesh ... -
How a nonconvergent recovered Hessian works in mesh adaptation
(Society for Industrial and Applied Mathematics, 2014-01-01)Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian from a linear finite element approximation ... -
Conditioning of finite element equations with arbitrary anisotropic meshes
(American Mathematical Society, 2014-03-05)Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first factor is proportional to a power of ... -
When is Jones' Space Normal?
(American Mathematical Society, 1975-07-01) -
The Character of omega 1 in First Countable Spaces
(American Mathematical Society, 1977-01-01) -
Some Spaces Related to Topological Inequalities Proven by the Erdös-Rado Theorem
(American Mathematical Society, 1978-09-01) -
An Axiom for Nonseparable Borel Theory
(American Mathematical Society, 1979-07-01)
