We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on finite-dimensional space minimization least-squares residual. Since involves solution equations, it not accesable, and replaced by an approximation obtained elements. This results into perturbed method. (a posterio...

Frequency domain formulations of computational electromagnetic problems often require the solutions of complex-valued non-Hermitian systems of equations, which are still symmetric. For this kind of problems a whole class of sub-variant solver methods derived from the complex-valued Bi-Conjugate Gradient method is available. This class of methods contains established solution methods as the Conj...

It is shown how various ideas that are well established for the solution of Poisson’s equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns out to be particularly fruitful. We propose a modified multigrid V cycle scheme that is not only much simpler, but also more efficient than the standard V cy...

in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functi...

AbRtract This paper deals with the domain decomposition-based preconditioned conjugate gradient method. The Schur complement is expressed as a function of & simple interface matrix. This function is approximated by a simple rational function to generate a simple matrix that is then used 8.8 & preconditioner for the Schur complement. Extensive experiments are performed to examine the effectivene...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

This paper is concerned with the numerical solution of a Karush–Kuhn– Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior–Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation deta...

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = ∑ aij(x)uxixj + ∑ bi(x)uxi + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the res...

A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh size...

We present an efficient multigrid algorithm that is adequate to solve a heavy linear system given in cloth simulation. Although multigrid has been successfully applied to the Poisson problems, it is hard to migrate to complicated cloth deformations due to its lack of physical meaning in level construction. We addresses this problem by developing a physically faithful technique ensuring the cons...