Advancing analysis capabilities in ANSYS through solver technology.
We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.
An alternating-direction iterative procedure is described for a class of Helmholz-like problems. An algorithm for the selection of the iteration parameters is derived; the parameters are complex with some having positive real part and some negative, reflecting the noncoercivity and nonsymmetry of the finite element or finite difference matrix. Examples are presented, with an applications to wave propagation.