A fictitious domain method for acoustic wave propagation problems

Based on the essence of Lagrange multiplier, a fictitious domain method, especially for acoustic wave propagation problems in exterior domain, is proposed, where all computational tasks are carried out in an auxiliary simply shaped domain, and the original domain is embedded into it. The simplicity of the auxiliary domain enables us to use uniform meshes to construct the finite element space and form a special structured stiffness matrix. Finally, the stability, convergence and error estimates are obtained for the numerical schemes.