@Article{DominguesRousSchn:2009:AdMuMe,
               author = "Domingues, Margarete Oliveira and Roussel, Olivier and Schneider, 
                         Kai",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "An adaptive multiresolution method for parabolic PDEs with 
                         time-step control",
              journal = "International Journal for Numerical Methods in Engineering",
                 year = "2009",
               volume = "78",
               number = "6",
                pages = "652--670",
                 note = "{Setores de Atividade: Transporte A{\'e}reo.}",
             keywords = "adaptivity, multiresolution, finite volume, Runge–Kutta, partial 
                         differential equation, time-step control.",
             abstract = "We present an efficient adaptive numerical scheme for parabolic 
                         partial differential equations based on a finite volume (FV) 
                         discretization with explicit time discretization using embedded 
                         RungeKutta (RK) schemes. A multiresolution strategy allows local 
                         grid refinement while controlling the approximation error in 
                         space. The costly fluxes are evaluated on the adaptive grid only. 
                         Compact RK methods of second and third order are then used to 
                         choose automatically the new time step while controlling the 
                         approximation error in time. Non-admissible choices of the time 
                         step are avoided by limiting its variation. The implementation of 
                         the multiresolution representation uses a dynamic tree data 
                         structure, which allows memory compression and CPU time reduction. 
                         This new numerical scheme is validated using different classical 
                         test problems in one, two and three space dimensions. The gain in 
                         memory and CPU time with respect to the FV scheme on a regular 
                         grid is reported, which demonstrates the efficiency of the new 
                         method.",
                  doi = "10.1002/nme.2501",
                  url = "http://dx.doi.org/10.1002/nme.2501",
                 issn = "0029-5981 and 1097-0207",
                label = "lattes: 4693848330845067 1 DominguesRousSchn:2009:AdMuMe",
           targetfile = "2501_ftp.pdf",
        urlaccessdate = "19 maio 2024"
}