The main theme of the book centers around adaptive numerical schemes for conservation laws based on a concept of multiresolution analysis. Efficient algorithms are presented for implementing this program for finite volume schemes on unstructured grids for general systems of multidimensional hyperbolic conservation laws. The efficiency is verified for several realistic numerical test examples. In addition, a rather thorough error analysis is supporting the approach. The monograph covers material ranging from the mathematical theory of conservation laws to the nitty-gritty of hash tables and memory management for an actual implementation. This makes it a self-contained book for both numerical analysts interested in the construction and the theory of adapative finite volume schemes as well as for those looking for a detailed guide on how to design and implement adaptive wavelet based solvers for real world problems. Since modern techniques are presented in an appealing way, the material is also well suited for an advanced course in numerical mathematics.
Adaptive Multiscale Schemes for Conservation Laws
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Inside This Book
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First Sentence:
The objective of this chapter is the introduction of conservation laws and how to approximate their solution. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
box wavelets, multiscale transformation, mask matrices, local index sets, higher vanishing moments, primal wavelets, graded tree, locally uniform grid, curvilinear case, stable completion, grid hierarchy, perturbation error, adaptive grid, mask coefficients, numerical fluxes, flux evaluation, old time level, shock reflection, grading parameter, multiscale decomposition, refinement criterion, refinement levels, hash maps, new time level, wavelet types New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The objective of this chapter is the introduction of conservation laws and how to approximate their solution. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
box wavelets, multiscale transformation, mask matrices, local index sets, higher vanishing moments, primal wavelets, graded tree, locally uniform grid, curvilinear case, stable completion, grid hierarchy, perturbation error, adaptive grid, mask coefficients, numerical fluxes, flux evaluation, old time level, shock reflection, grading parameter, multiscale decomposition, refinement criterion, refinement levels, hash maps, new time level, wavelet types New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
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- Boundary Value Problems, Fifth Edition: and Partial Differential Equations by David L. Powers in Back Matter
- Numerical Methods in Computational Electrodynamics by Ursula van Rienen in Back Matter
- Introduction to Numerical Analysis by J. Stoer in Back Matter
- Advances in Software Tools for Scientific Computing (Lecture Notes in Computational Science and Engineering) by Hans P. Langtangen in Back Matter
- Numerical Analysis (Mathematics) by Lee W. Johnson in Back Matter
See all 23 books this book cites
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