Beräkningsmetoder för andra ordningens vågekvationer med inbäddade ränder

Tidsperiod: 2015-01-01 till 2018-12-31

Projektledare: Gunilla Kreiss

Finansiär: Vetenskapsrådet

Bidragstyp: Projektbidrag

Budget: 3 000 000 SEK

This project concerns computational methods for wave propagation problems. We propose to develop efficient and accurate techniques to implement important boundary and/or interface conditions for second order wave equations without aligning the computational grid to boundaries and interfaces. The aim is a high order accurate, computationally efficient, finite element method. We will in particular consider the scalar wave equation and the system of elastic wave equations in the linear, compressible case, and applications in acoustics and the geological sciences. To achieve high accuracy and efficiancy we will use a structured, equidistant partitioning of the domain, and high order elements. In all realistic settings boundaries will not align with element faces. We will use ideas from the so called Nitsche fictitious domain methods for elliptic problems, were boundary conditions are imposed weakly by including penalty terms in the weak formulation. The methodology will be implemented in the open source software library deal.II.