Projects per year
Abstract
We prove that the standard secondkind integral equation formulation of the exterior Dirichlet problem for the Helmholtz equation is coercive (i.e., signdefinite) for all smooth convex domains when the wavenumber k is sufficiently large. (This integral equation involves the socalled combined potential, or combined field, operator.) This coercivity result yields kexplicit error estimates when the integral equation is solved using the Galerkin method, regardless of the particular approximation space used (and thus these error estimates apply to several hybrid numericalasymptotic methods developed recently). Coercivity also gives kexplicit bounds on the number of GMRES iterations needed to achieve a prescribed accuracy when the integral equation is solved using the Galerkin method with standard piecewisepolynomial subspaces. The coercivity result is obtained by using identities for the Helmholtz equation originally introduced by Morawetz in her work on the local energy decay of solutions to the wave equation
Original language  English 

Pages (fromto)  15871639 
Number of pages  53 
Journal  Communications on Pure and Applied Mathematics 
Volume  68 
Issue number  9 
Early online date  6 Oct 2014 
DOIs  
Publication status  Published  1 Sep 2015 
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Projects
 2 Finished

Post Doc Fellowship  New Methods and Analysis for Wave Propagation Problems
Engineering and Physical Sciences Research Council
1/04/11 → 31/03/14
Project: Research council

Boundary Integral Equation Methods for HF Scattering Problems
Graham, I. & Smyshlyaev, V. P.
Engineering and Physical Sciences Research Council
24/03/09 → 23/09/12
Project: Research council
Profiles

Euan Spence
 Department of Mathematical Sciences  Professor
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching