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Acoustic singular surfaces in an exponential class of inhomogeneous gases: A new numerical approach based on Krylov subspace spectral methodologies
Bailey Rester, James V. Lambers, Pedro M. Jordan
We investigate the propagation of acoustic singular surfaces, specifically, linear shock waves and nonlinear acceleration waves, in a class of inhomogeneous gases whose ambient mas…
Convergence Analysis of a Krylov Subspace Spectral Method for the 1-D Wave Equation in an Inhomogeneous Medium
Bailey Rester, Anzhelika Vasilyeva, James V. Lambers
This paper presents a convergence analysis of a Krylov subspace spectral (KSS) method applied to a 1-D wave equation in an inhomogeneous medium. It will be shown that for sufficien…
Numerical Solution of an Extra-wide Angle Parabolic Equation through Diagonalization of a 1-D Indefinite Schrödinger Operator with a Piecewise Constant Potential
Sarah D. Wright, James V. Lambers
We present a numerical method for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, t…
Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices
Amber S. Robertson, James V. Lambers
In this paper we examine iterative methods for solving the forward () and adjoint () systems of linear equations used to approximate the sca…