142 research outputs found
Numerical Solutions for the Simulation of Monolithic Microwave Integrated Circuits
The electric properties of monolithic microwave integrated circuits can be described in terms of their scattering matrix using Maxwellian equations. The corresponding three-dimensional boundary value problem of Maxwell's equations can be solved by means of a finite-volume scheme in the frequency domain. This results in a two-step procedure: a time and memory consuming eigenvalue problem for nonsymmetric matrices and the solution of a large-scale system of linear equations with indefinite symmetric matrices. Improved numerical solutions for these two linear algebraic problems are treated
Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides
A new approach is discussed for solving large nonsymmetric systems of linear
equations with multiple right-hand sides. The first system is solved with a
deflated GMRES method that generates eigenvector information at the same time
that the linear equations are solved. Subsequent systems are solved by
combining restarted GMRES with a projection over the previously determined
eigenvectors. This approach offers an alternative to block methods, and it can
also be combined with a block method. It is useful when there are a limited
number of small eigenvalues that slow the convergence. An example is given
showing significant improvement for a problem from quantum chromodynamics. The
second and subsequent right-hand sides are solved much quicker than without the
deflation. This new approach is relatively simple to implement and is very
efficient compared to other deflation methods.Comment: 13 pages, 5 figure
Perfectly matched layers in transmission lines
The field distribution at the ports of the transmission line structure is computed by applying Maxwell's equations to the structure and solving an eigenvalue problem. The high dimensional sparse system matrix is complex in the presence of losses and Perfectly Matched Layer. A method is presented which preserves sparseness and delivers only the small number of interesting modes out with the smallest attenuation. The modes are found solving a sequence of eigenvalue problems of modified matrices with the aid of the invert mode of the Arnoldi iteration using shifts. A new strategy is described which allows the application of the method, first developed for microwave structures, to optoelectronic devices
Large-scale computation of pseudospectra using ARPACK and eigs
ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000
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