Adaptive Wavelet Representation And Differentiation On Block-structured Grids

This paper considers a new adaptive wavelet solver for two-dimensional systems based on an adaptive block refinement (ABR) method that takes advantage of the quadtree structure of dyadic blocks in rectangular regions of the plane. The computational domain is formed by non-overlapping blocks. Each block is a uniform grid, but the step size may change from one block to another. The blocks are not predetermined, but they are dynamically constructed according to the refinement needs of the numerical solution. The decision over whether a block should be refined or unrefined is taken by looking at the magnitude of wavelet coefficients of the numerical solution on such block. The wavelet coefficients are defined as differences between values interpolated from a coarser level and known function values at the finer level. The main objective of this paper is to establish a general framework for the construction and operation on such adaptive block-grids in 2D. The algorithms and data structure are formulated by using abstract concepts borrowed from quaternary trees. This procedure helps in the understanding of the method and simplifies its computational implementation. The ability of the method is demonstrated by solving some typical test problems. © 2003 IMACS. Published by Elsevier B.V. All rights reserved.4703/04/15421437Cohen, A., Wavelet methods in numerical analysis (2000) Handbook of Numerical Analysis, 7. , P.G. Ciarlet, LionsJ.L. Amsterdam: ElsevierHolmström, M., (1997) Wavelet Based Methods for Time Dependent PDEs, , Ph.D. Thesis, Uppsala UniversityWalden, J., A general adaptive solver for hyperbolic PDEs based on filter bank subdivisions (2000) Appl. Numer. Math., 33 (1-4), pp. 317-325Vasilyev, O.V., Browman, C., Second generation wavelet collocation method for the solution of partial differential equations (2000) J. Comput. Phys., 165, pp. 660-693Knuth, D.E., (1997) The Art of Programming, , Reading, MA: Addison-WesleyHunter, G.M., Steiglitz, K., Operations on images using quad trees (1979) IEEE Trans. Pattern Anal. Mach. Intell., PAMI-1 (2), pp. 145-153Tromper, R.A., Verwer, J.G., Runge-Kutta methods and local uniform grid refinement (1993) Math. Comput., 60 (202), pp. 591-616Bacry, E., Mallat, S., Papanicolau, G., A wavelet based space-time adaptive numerical method for partial equations (1992) Math. Model. Numer. Anal., 26 (7), pp. 793-834Lötstedt, P., Söderberg, S., Ramage, A., Hemmingsson-Frändén, L., Implicit solution of hyperbolic equations with space-time adaptivity (2002) BIT, 42, pp. 134-158Glowinski, R., Pan, T.-W., Périaux, J., A fictitious domain method for Dirichlet problem and application (1994) Comput. Methods Appl. Mech. Engrg., 111, pp. 283-303Koshigoe, H., Kitahara, K., Finite difference method with fictitious domain applied to a Dirichlet problem (2001) 12th Conference on Domain Decomposition Methods, pp. 151-163. , T. Chan, T. Kako, H. Kawarada, & O. Pironneau. DDM.orgKunoth, A., Wavelet techniques for the fictitious domain - Lagrange multiplier approach (2001) Numer. Algorithms, 27, pp. 291-316Rieder, A., Embedding and a priori wavelet-adaptivity for Dirichlet problems (2000) Modél. Math. Anal. Numér., 34 (6), pp. 1189-120

A Importância Estratégica Do Gás Natural Como Matéria-prima Para O Pólo Industrial De Camaçari-ba

[No abstract available]231-312513

An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction

We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge–Kutta scheme for time integration. Harten's cell average multiresolution allows to introduce a locally refined spatial mesh while controlling the error. The incompressibility of the magnetic field is controlled by using a Generalized Lagrangian Multiplier (GLM) approach with a mixed hyperbolic–parabolic correction. Different applications to two-dimensional problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a regular fine mesh

Adaptive Finite Difference Schemes Based On Interpolating Wavelets For Solving 2d Maxwell's Equations

[No abstract available]36003603Yee, K.S., Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in isotropic Media (1966) IEEE Trans. Antennas and Propagation, 14, pp. 302-307. , AprilHolmstrom, M., Wavelet based methods for time dependent PDEs (1997), Ph.D. dissertation, Uppsala UniversityP. Pinho, M. O. Domingues, P. J. S. G. Ferreira, S. M. Gomes, A. Gomide and J. R. Pereira' Interpolating wavelets and adaptive finite difference schemes for solving Maxwell's equations, 2006. Acceptd for publication on the IEEE Transactions on MagneticsDomingues, M.O., Ferreira, P.J.S.G., Gomes, S.M., Gomide, A., Pereira, J.R., Pinho, P., High Order Finite-Difference Schemes for Maxwell's Equations, 2006, , Submmite