Domain Decomposition with Fusion Frames
In computational acoustics the goal is to find a numerical solution of physical equations, like the Helmholtz equation. Traditionally, this is done by the boundary element or finite element method. To reduce the computational load the operator equation is split. The domain decomposition methods solves a boundary value problem by splitting it into smaller boundary problems on subdomains. It is vital to find the most applicable and tractable overlapping or non-overlapping domain decomposition for dividing a large problem to smaller one.One of the most important problems in this method is the splitting the given space and finding the global solution from the local ones, in particular in the overlapping domain case.In this paper, we approach this problem by using fusion frames, therefore allowing overlapping. At least in a mathematical setting fusion frames allows to find more numerically tractable approach on subdomains and combine the solution on the subspaces to get the global solution. We can apply this idea for operator equations and present several discretization by fusion frames and their duals and analyze their numerical efficiency.