To this end, we conduct a survey of semi-Lagrangian eikonal solvers, and develop new, efficient, first order solvers for the eikonal equation in 3D called ordered line integral methods (OLIMs). Motivated by the requirements of sound propagation simulations, we introduce higher order semi-Lagrangian eikonal solvers which we term jet marching methods (JMMs). JMMs additionally transport higher order derivative information causally, allowing the eikonal equation to be solved to high order using compact stencils. To solve the transport equation, we apply paraxial raytracing to propagate the amplitude along each local ray. We first develop a JMM that handles a smoothly varying speed of sound on a regular grid in 2D. To conform to the requirements of industrial room acoustics applications, we develop a second order JMM for computing the eikonal on a tetrahedron mesh with a constant speed of sound. We compute multiple arrivals by reinitializing the eikonal equation on reflecting walls and diffracting edges. We use dynamic programming to enforce reflection and diffraction boundary conditions for these scattered fields in the semi-Lagrangian setting, requiring the use of the uniform theory of diffraction. Along the way, we carry out numerical analysis of our solvers, and conduct extensive tests.
Dean's rep: Dr. P.S. Krishnaprasad
Members: Dr. Ramani Duraiswami
Dr. Howard Elman
Samuel Potter is a PhD candidate in computer science at the University of Maryland, College Park, advised by Profs. Maria Cameron and Ramani Duraiswami. His research interests are in scientific computing, numerical analysis, and spatial audio. His current research focus is high-frequency wave propagation for precomputed room acoustics. He will start a position as a Courant Instructor at the Courant Institute of Mathematical Sciences at New York University in Fall 2021.