A conforming multi-domain Legendre spectral method for solving diffusive-viscous wave equations in the exterior domain with separated star-shaped obstacles

Abstract In this paper, we propose a conforming multi-domain spectral method that combines mapping techniques to solve the diffusive-viscous wave equation in the exterior domain of two complex obstacles. First, we confine the exterior domain within a relatively large rectangular computational domain. Then, we decompose the rectangular domain into two sub-domains, each containing one obstacle. By applying coordinate transformations along radial direction to each sub-domain, we map them into eight regular sub-blocks. Subsequently, we perform numerical simulations using classical spectral methods on these regular sub-blocks. Our analysis focuses on the optimal convergence of this approach. The numerical results demonstrate the high-order accuracy of the proposed method.