David W. Zingg

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This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce(More)
Diagonal-norm summation-by-parts (SBP) operators can be used to construct timestable high-order accurate finite-difference schemes. However, to achieve both stability and accuracy, these operators must use s-order accurate boundary closures when the interior scheme is 2s-order accurate. The boundary closure limits the solution to (s + 1)-order global(More)
A Newton–Krylov algorithm is presented for two-dimensional Navier–Stokes aerodynamic shape optimization problems. The algorithm is applied to both the discrete-adjoint and the discrete  ow-sensitivity methods for calculating the gradient of the objective function. The adjoint and  ow-sensitivity equations are solved using a novel preconditioned(More)
Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. The SBP operator definition includes a weight matrix that is used formally for discrete integration; however, the accuracy of the weight matrix as a quadrature rule is not explicitly part of the SBP definition. We show that SBP weight matrices are related to(More)
High-accuracy finite-difference schemes are used to solve the two-dimensional timedomain Maxwell equations for electromagnetic wave propagation and scattering. The high-accuracy schemes consist of a seven-point spatial operator coupled with a six-stage Runge–Kutta time-marching method. Two methods are studied, one of which produces the maximum order of(More)
A gradient-based Newton–Krylov algorithm is presented for the aerodynamic shape optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier–Stokes equations in conjunction with a one-equation transport turbulence model. The preconditioned generalized minimal residual method is applied to solve the(More)
There is a need for flexible iterative solvers that can solve large-scale (> 106 unknowns) nonsymmetric sparse linear systems to a small tolerance. Among flexible solvers, flexible GMRES (FGMRES) is attractive because it minimizes the residual norm over a particular subspace. In practice, FGMRES is often restarted periodically to keep memory and work(More)