adaptive multiresolution methods

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ID: 201818
2011
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Abstract
These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries. The discretization schemes are based either on finite volume or finite difference schemes. The concept of multiresolution analyses, including Harten’s approach for point and cell averages, is described in some detail. Then the sparse point representation method is discussed. Different strategies for adaptive time-stepping, like local scale dependent time stepping and time step control, are presented. Numerous numerical examples in one, two and three space dimensions validate the adaptive schemes and illustrate the accuracy and the gain in computational efficiency in terms of CPU time and memory requirements. Another aspect, modeling of turbulent flows using multiresolution decompositions, the so-called Coherent Vortex Simulation approach is also described and examples are given for computations of three-dimensional weakly compressible mixing layers. Most of the material concerning applications to PDEs is assembled and adapted from previous publications [27, 31, 32, 34, 67, 69].
Reference Key
kai2011esaim:adaptive Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Schneider Kai;Roussel Olivier;Gomes Sônia M.;Domingues Margarete O.
Journal games for health journal
Year 2011
DOI
10.1051/proc/201134001
URL
http://dx.doi.org/10.1051/proc/201134001
Keywords
applied mathematics quantitative methodsmathematics

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