# Adaptive multiresolution methods

Margarete O. Domingues; Sônia M. Gomes; Olivier Roussel; Kai Schneider

ESAIM: Proceedings (2011)

- Volume: 34, page 1-96
- ISSN: 1270-900X

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topDomingues, Margarete O., et al. Louvet, Violaine, and Massot, Marc, eds. "Adaptive multiresolution methods." ESAIM: Proceedings 34 (2011): 1-96. <http://eudml.org/doc/251268>.

@article{Domingues2011,

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].},

author = {Domingues, Margarete O., Gomes, Sônia M., Roussel, Olivier, Schneider, Kai},

editor = {Louvet, Violaine, Massot, Marc},

journal = {ESAIM: Proceedings},

language = {eng},

month = {12},

pages = {1-96},

publisher = {EDP Sciences},

title = {Adaptive multiresolution methods},

url = {http://eudml.org/doc/251268},

volume = {34},

year = {2011},

}

TY - JOUR

AU - Domingues, Margarete O.

AU - Gomes, Sônia M.

AU - Roussel, Olivier

AU - Schneider, Kai

AU - Louvet, Violaine

AU - Massot, Marc

TI - Adaptive multiresolution methods

JO - ESAIM: Proceedings

DA - 2011/12//

PB - EDP Sciences

VL - 34

SP - 1

EP - 96

AB - 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].

LA - eng

UR - http://eudml.org/doc/251268

ER -

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