Is the Helmholtz Equation Really Sign-Indefinite?
                    
                        
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منابع مشابه
Is the Helmholtz Equation Really Sign-Indefinite?
The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at certain wavenumbers (those that correspon...
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We use the method of layer potentials to study interior and exterior Dirichlet and Neumann problems for the Helmholtz equation ((+k 2)u = 0 on a Lipschitz domain for all wave number k 2C with Im k 0. Following the approach for the case of smooth boundary 3], we pursue as solution a single layer potential for Neumann problem or a double layer potential for Dirichlet problem. The lack of smoothne...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2014
ISSN: 0036-1445,1095-7200
DOI: 10.1137/120901301