Journal ArticleDOI
Adaptive biorthogonal spline schemes for advection-reaction equations
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TLDR
This paper uses biorthogonal spline wavelets to develop numerical schemes for multidimensional advection-reaction equations that have the ability to carry out adaptive compression while preserving the total mass.About:
This article is published in Journal of Computational Physics.The article was published on 2004-01-01. It has received 8 citations till now. The article focuses on the topics: Biorthogonal system & Rate of convergence.read more
Citations
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Journal ArticleDOI
Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering
G. Hariharan,K. Kannan +1 more
TL;DR: It is shown that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations and future scope and directions involved in developing wavelet algorithm for solving reaction– Diffusion equations are addressed.
Journal ArticleDOI
Wavelet-based surrogate time series for multiscale simulation of heterogeneous catalysis
Sourav Gur,Thomas Danielson,Thomas Danielson,Qingang Xiong,Celine Hin,Sreekanth Pannala,George N. Frantziskonis,Aditya Savara,C. Stuart Daw +8 more
TL;DR: A wavelet-based scheme that encodes the essential dynamics of discrete microscale surface reactions in a form that can be coupled with continuum macroscale flow simulations with high computational efficiency makes it possible to simulate the dynamic behavior of reactor-scale heterogeneous catalysis without requiring detailed concurrent simulations at both the surface and continuum scales.
Journal ArticleDOI
Space-time least-squares finite element method for convection-reaction system with transformed variables
TL;DR: A method to solve a convection-reaction system based on a least-squares finite element method (LSFEM) and proposes a quadratic transformation of variables to prevent the computed hemoglobin concentration becoming negative in certain regions of the flow.
Journal ArticleDOI
A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals
TL;DR: In this article, a numerical method based on the wavelet theory is developed for calculating band structures of 2D phononic crystals consisting of general anisotropic materials, and two types of wavelets, the Haar wavelet and Biorthogonal wavelet, are selected.
Journal ArticleDOI
Solving singularly perturbed advection–reaction equations via non-standard finite difference methods
TL;DR: In this article, the authors design and implement two non-standard finite difference methods (NSFDMs) to solve singularly perturbed advection-reaction equations (SPARE).
References
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
Journal ArticleDOI
Über die partiellen Differenzengleichungen der mathematischen Physik
TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.