Mécanique Analytique (Cambridge Library Collection - Mathematics) (French Edition)

Multileveladaptivemethodsplayanincreasinglyimportantroleinthesolutionofmanyscientificandengineeringproblems.Fastadaptivemethodstechniquesarewidelyusedbyspecialiststoexecuteandanalyzesimulationandoptimizationproblems.Thismonographpresentsaunifiedapproachtoadaptivemethods,addressingtheirmathematicaltheory,efficientalgorithms,andflexibledatastructures.Rüdeintroducesawell-foundedmathematicaltheorythatleadstointelligent,adaptivealgorithms,andsuggestsadvancedsoftwaretechniques.Thisnewkindofmultigridtheorysupportstheso-called'BPX'and'multilevelSchwarz'methods,andleadstothediscoveryoffastermorerobustalgorithms.Thesetechniquesaredeeplyrootedinthetheoryoffunctionspaces.MathematicalandComputationalTechniquesforMultilevelAdaptiveMethodsexaminesthisdevelopmenttogetherwithitsimplicationsforrelevantalgorithmsforadaptivePDEmethods.Theauthorshowshowabstractdatatypesandobject-orientedprogrammingcanbeusedforimprovedimplementation.