The paper demonstrates the model order reduction procedures applied to semiconductor devices with multiple heat sources. The approach is demonstrated for a device with nine heat sources where some of them are permanently active and other work under switching conditions. For the order reduction the software package MOR for ANSYS is used, which is based on the Krylov subspace method via the Arnol...

The methods of Arnoldi and Lanczos are used for solving large and sparse eigenvalue problems. Such problems arise in the computation of stability of solutions of parameter-dependent, nonlinear partial differential equations discretized by the GalerkiQinite element method. Results are presented for the stability of equilibrium solutions of axisymmetric ferromagnetic liquid interfaces in external...

We consider the problem of computing PageRank. The matrix involved is large and cannot be factored, and hence techniques based on matrix-vector products must be applied. A variant of the restarted refined Arnoldi method is proposed, which does not involve Ritz value computations. Numerical examples illustrate the performance and convergence behavior of the algorithm. AMS subject classification ...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...

Forward transient electromagnetic modeling requires the numerical solution of a linear constant-coefficient initial-value problem for the quasi-static Maxwell equations. After discretization in space this problem reduces to a large system of ordinary differential equations, which is typically solved using finite-difference time-stepping. We compare standard time-stepping schemes such as the exp...

This work examines the effects of uncertain material and geometry properties on the dynamic characteristics of a simply supported plate. The forced responses of the plate are predicted using the polynomial chaos expansion method. The stochastic system equations are transformed to a set of deterministic equations using Galerkin projection. In order to improve the computational efficiency when at...

We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the tensor infinite Arnoldi method (TIAR), which is applicable to a general class of NEPs, and we show how to specialize the algorithm to a specific NEP: the wavegui...

Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present a heuristic for the automated pole selection when the function to be approximated is of Markov type, such as the matrix square root. The performance of this approach is demons...

This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.

where T (λ) ∈ R is a family of symmetric matrices depending on a parameter λ ∈ J , and J ⊂ R is an open interval which may be unbounded. As in the linear case T (λ) = λI −A a parameter λ is called an eigenvalue of T (·) if problem (1) has a nontrivial solution x 6= 0 which is called a corresponding eigenvector. We assume that the matrices T (λ) are large and sparse. For sparse linear eigenvalue...