-In this paper the regulator and filter algebraic Riccati equations, corresponding to the steady state optimal control and filtering of weakly coupled linear discrete stochastic systems are solved in terms of reduced-order sub problems by using the eigenvector approach. The eigenvector method outperforms iterative methods (fixed point iterations, Newton method) of solutions to reduced-order sub...

This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions. This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints. The integral constraint is included in the cost by a penalty term whereas the bilateral control constraints are handled explicit...

A derivative-free Quasi-Newton (DFQN) method previously published [J. Greenstadt, Math. Comp., v. 26, 1972, pp. 145—166] has been revised and simplified. The main modification has the effect of keeping all the successive approximants to the Hessian matrix positive-definite. This, coupled with some improvements in the line search, has enhanced the performance of the method considerably. The resu...

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares tec...

We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretised by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviour but also regardin...

A new fully-variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [10] that involves using Newton’s method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equat...

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for p...

We develop a parallel scalable domain decomposition method for the simulation 9 of blood flows in compliant arteries in 3D, by using a fully coupled system of linear elasticity 10 equation and incompressible Navier-Stokes equations. The system is discretized with a finite 11 element method on unstructured moving meshes and solved by a Newton-Krylov algorithm 12 preconditioned with an overlappin...

The purpose of this paper is to discuss in detail the use of scalar matter coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum gravity in the restricted setting provided by this symmetry reduction of general relativity. We will obtain the relevant Hamiltonian and quantize it with the techniques already used for the purely gravitational case. Finally, we will discuss t...

Exact moment equations for nonlinear Itô processes are derived. Taylor expansion of the drift and diffusion coefficients around the first conditional moment gives a hierarchy of coupled moment equations which can be closed by truncation or a Gaussian assumption. The state transition density is expanded into a Hermite orthogonal series with leading Gaussian term and the Fourier coefficients are ...