The Boundary Element Method for the Helmholtz Equation ... - FEI VÅ B

List of SymbolsR – Set of real numbersR + – Set of positive real numbersN – Set of natural numbersN 0 – Set of natural numbers including zeroC – Set of complex numbersRe z – Real part of a complex number zIm z – Imaginary part of a complex number zi – Imaginary unit∥ · ∥ – Euclidian norm in R n and C n∥ · ∥ X – Norm in a linear space X⟨·, ·⟩ – Euclidian inner product in R n and C n⟨·, ·⟩ – Functional value⟨·, ·⟩ X – Inner product in a linear space XIm V – Image of an operator VL(X, Y ) – Space of linear continuous mappings from X to Y(X) ∗ – Dual space to X, i.e., L(X, C)∇u – Gradient of a function u∆ – Laplace operatorγ 0,int – Interior Dirichlet trace operatorγ 1,int – Interior Neumann trace operatorγ 0,ext – Exterior Dirichlet trace operatorγ 1,ext – Exterior Neumann trace operatorI – Identity operatorv κ – Fundamental solution for the Helmholtz equation