2015/05/09 by Luca Bonaventura, Bonaventura, Luca
Computer Science · Engineering · Mathematics · Physics and Astronomy · #65L04 #65M08 #65M20 #65Z05 #86A10 #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #cs.NA #math.NA #msc:65L04 #msc:65M08 #msc:65M20 #msc:65Z05 #msc:86A10 #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1505.02248
arxiv created 2015/05/09 · openalex publication_date 2015/05/09 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain decomposition technique is outlined, that allows to replace the computation of a global exponential matrix by a number of independent and easily parallelizable local problems. Advantages and potential problems of the proposed technique are discussed. Numerical experiments on simple, yet relevant model problems show that the resulting method allows to increase computational efficiency with respect to standard implementations of exponential methods.