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- Domain Decomposition methods for the high frequency Helmholtz equation
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- Home
- Our school
- Study with us
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-
Student life & resources
Postgraduate research
- Info for new students
- Current research students
- Postgraduate conference
- Postgraduate events
- Postgraduate student awards
- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
- Enrolment variation
- Changing tutorials
- Illness or misadventure
- Application form for existing casual tutors
- ARC grants Head of School sign off
- Computing facilities
- Choosing your major
- Engage with us
- News & events
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Abstract:
When solving the linear space-time wave equation in the band limited case, it is attractive to reduce the problem to one in space only by applying the Fourier transform in time. The result is the Helmholtz equation, a second order PDE in space which is not coercive in standard settings. Its discretization yields large frequency-dependent non-normal complex linear systems which are notoriously hard to solve, especially in the high frequency case. Because of the size of the systems, iterative methods are often required.
In the talk we describe a new multilevel domain decomposition method for efficiently solving these systems iteratively and we outline its convergence theory. This involves:
- the analysis of nearby problems with artificial absorption;
- a non-standard projection-theoretic setting for domain decomposition and
- the ``field of values'' analysis of the convergence of Krylov iterative methods.
All theory known at the present assumes the wave speed is constant. We also describe some recent progress in the removal of this assumption.
The talk is joint work with Euan Spence, Eero Vainikko and Stefan Sauter.