We present simultaneous pseudo-timestepping as an efficient method for aerodynamic shape optimization. In this method, instead of solving the necessary optimality conditions by iterative techniques, pseudo-time embedded nonstationary system is integrated in time until a steady state is reached. The main advantages of this method are that it requires no additional globalization techniques and th...

We propose and study a new parallel one-shot Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithm for shape optimization problems constrained by steady incompressible NavierStokes equations discretized by finite element methods on unstructured moving meshes. Most existing algorithms for shape optimization problems solve iteratively the three components of the optimality system: the state equations ...

A general method based on adjoint formulation is discussed for the optimal control of distributed parameter systems (including boundary parameter) which is especially suitable for large dimensional control problems. Strategies for efficient and robust implementation of the method are described. The method is applied to the problem of controlling vortex shedding behind a cylinder (through suctio...

In the paper the one-dimensional one-center scattering problem with the initial potential α|x|−1 on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as necessary conditions in the singular point alongside with account of the analytical structure of fundamental solutions, it allows us to receive exact expressions for the wa...

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schrödinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quan...

2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

Koren, B. and P.W. Hemker, Damped, direction-dependent multigrid for hypersonic flow computations, Applied Numerical Mathematics 7 (1991) 309-328. A nonlinear multigrid technique with improved robustness is developed for the solution of the steady Euler equations. The system of nonlinear equations is discretized by an upwind finite volume method. Collective symmetric point Gauss-Seidel relaxati...

Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In [25], we have introduced a hybrid mixed method for the compressible Navier-Stokes equations as a combination of a hybridized DG scheme for the convective terms, and an H(div,Ω)-method fo...

The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. We show that ensemble sensitivity is proportional to the projection of the analysis-error covariance onto the adjoint sensitivity field...