Ομιλητής : Lehel Banjai
Ημερομηνία, ώρα : Παρασκευή 18 Οκτωβρίου 2024, 10:45
Τοποθεσία : Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.
Τίτλος : “Numerical methods for the fractional Helmholtz equation”.
Περίληψη : “In this talk we consider the Helmholtz equation where the usual Laplacian is replaced by a non-local variant: the spectral fractional Laplacian. The thus obtained fractional Helmholtz equation has applications to geophysical electromagnetics, but in this talk we focus on the development and analysis of efficient numerical methods. We describe and analyse two possible approaches. Firstly, a direct contour integral method discretised by a sinc quadrature combined with an hp-finite element method. Secondly a tensor product hp-finite element method applied to an equivalent local problem in a spatially extended domain. In both cases we show that the cost is equivalent to solving a single standard Helmholtz equation and a fractional Poisson problem. The talk ends with numerical experiments showing exponential convergence of both approaches.”