TITLE:

SPECTRAL FFT-BASED INTEGRAL AND DIFFERENTIAL PDE SOLVERS FOR GENERAL DOMAINS

DATE:

Friday, January 29th, 2010

TIME:

3:00 PM

LOCATION:

Engineering Bldg. Room 300
21

SPEAKER:

Oscar Bruno, California Institute of Technology

ABSTRACT:

We present new methodologies for the numerical solution of Partial Differential Equations in general spatial domains. Based on a novel Fourier-Continuation (FC) method for the resolution of the Gibbs phenomenon, spectral surface-representation methods, fast high-order methods for evaluation of integral operators, and the well-known alternating direction approach, these methodologies give rise to fast and highly accurate frequency- and time-domain solvers for PDEs on general spatial domains. Our fast integral algorithms can solve, with high-order accuracy, problems of electromagnetic and acoustic scattering for complex three-dimensional geometries – including, possibly, singular elements such as wires, corners, edges and open screens. Our differential solvers for time-dependent PDEs, in turn, are based on use of the well known Alternating Direction Implicit (ADI) algorithm in conjunction with the FC method. Unlike previous alternating direction methods of order higher than one, which can only deliver unconditional stability for rectangular domains, the present _spectral_ Fourier-Continuation Alternating-Direction (FC-AD) algorithm possesses the desirable property of _unconditional stability for general domains_; the computational time required by the algorithm to advance a solution by one time-step, in turn, grows in an essentially linear manner with the number of spatial discretization points used. A variety of applications of the FC-AD methodology to Parabolic, Elliptic and Hyperbolic PDEs demonstrate the unconditional stability and high-order convergence of the method, as well the very significant improvements it can provide over the accuracy and speed resulting from other approaches.

HOST:

Gustaaf (Guus) Jacobs

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