An Adaptive Multi-Point Fast Frequency Sweep for Large-Scale Finite Element Models

Schultschik, Alwin; Farle, Ortwin; Dyczij‐Edlinger, Romanus

doi:10.1109/tmag.2009.2012639

Cited by 23 publications

(25 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Its singular value decomposition can be written as (11) where is the rank determined based on accuracy requirement , which is no greater than . The procedure so far can be viewed as a multipoint-based model order reduction [15], but with a different approach proposed to control its convergence. This approach can also be used by existing model order reduction methods for solving deterministic problems to control convergence.…”

Section: A Proposed Fast Eigenvalue Solutionmentioning

confidence: 99%

“…Moreover, the proposed eigenvalue solver reduces the original large-scale eigenvalue problem to a small eigenvalue problem by deterministic solutions. Different from the model order reduction methods developed to solve deterministic problems, , in electromagnetics such as [13]- [15], the proposed method solves generalized eigenvalue problems and quadratic eigenvalue problems , where , , and are sparse matrices, denotes an eigenvalue, and is an eigenvector.…”

mentioning

confidence: 99%

See 1 more Smart Citation

A Deterministic-Solution Based Fast Eigenvalue Solver With Guaranteed Convergence for Finite-Element Based 3-D Electromagnetic Analysis

Sheng

Jiao

2013

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

A fast solution to both the quadratic eigenvalue problem and the generalized eigenvalue problem is developed for the finite-element based analysis of general 3-D electromagnetic problems. Given an arbitrary frequency band of interest, denoting the number of physically important eigenvalues for this band by , the proposed eigenvalue solution is capable of solving a significantly reduced eigenvalue problem of to find a complete set of eigenvalues and eigenvectors that are physically important for the given frequency band. In addition to bypassing the need of solving a large-scale eigenvalue problem of , withbeing the system matrix size, the reduced eigenvalue problem is constructed from solutions to a deterministic problem. As a result, the methods that have been developed to solve deterministic problems and their fast solvers can all be readily leveraged to solve eigenvalue problems. Moreover, the proposed fast eigenvalue solution has guaranteed convergence and controlled accuracy, which is theoretically proved in this paper. The solution is applicable to general 3-D problems where the structures are arbitrary, materials are inhomogeneous, and both dielectrics and conductors can be lossy. Applications to microwave devices, package structures, and on-chip integrated circuits have demonstrated the accuracy, efficiency, and convergence of the proposed fast eigenvalue solution.Index Terms-Deterministic solutions, eigenvalue solutions, electromagnetic analysis, fast solvers, finite element methods, generalized eigenvalue problems, quadratic eigenvalue problems.

show abstract

Section: A Proposed Fast Eigenvalue Solutionmentioning

confidence: 99%

mentioning

confidence: 99%

A Deterministic-Solution Based Fast Eigenvalue Solver With Guaranteed Convergence for Finite-Element Based 3-D Electromagnetic Analysis

Sheng

Jiao

2013

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…Generalizations to multiple inputs/outputs and modes are straight-forward (Schultschik et al, 2009). …”

Section: Mp-mormentioning

confidence: 99%

“…Driven problem As detailed in Schultschik et al (2009), FE models of passive microwave junctions lead to frequency-dependent systems of the form:…”

Section: Compel 306mentioning

confidence: 99%

Adaptive strategies for fast frequency sweeps

Konkel

Farle

Köhler

et al. 2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

View full text Add to dashboard Cite

Purpose - The purpose of this paper is to compare competing adaptive strategies for fast frequency sweeps for driven and waveguide-mode problems and give recommendations for practical implementations. Design/methodology/approach - The paper first summarizes the theory of adaptive strategies for multi-point (MP) sweeps and then evaluates the efficiency of such methods by means of numerical examples. Findings - The authors' numerical tests give clear evidence for exponential convergence. In the driven case, highly resonant structures lead to pronounced pre-asymptotic regions, followed by almost immediate convergence. Bisection and greedy point-placement methods behave similarly. Incremental indicators are trivial to implement and perform similarly well as residual-based methods. Research limitations/implications - While the underlying reduction methods can be extended to any kind of affine parameter-dependence, the numerical tests of this paper are for polynomial parameter-dependence only. Practical implications - The present paper describes self-adaptive point-placement methods and termination criteria to make MP frequency sweeps more efficient and fully automatic. Originality/value - The paper provides a self-adaptive strategy that is efficient and easy to implement. Moreover, it demonstrates that exponential convergence rates can be reached in practice

show abstract

“…There are two major classes of MOR techniques that differ in their respective choice of projection basis. Multi-point methods (Prud'homme et al, 2002;Schultschik et al, 2009) are based on the FE solutions at a set of frequency points. They are robust and easy to implement but still require the FE matrix to be factorized multiple times.…”

mentioning

confidence: 99%

Efficient Fast Frequency Sweep Without Nonphysical Resonances

Farle¹,

Lösch²,

Dyczij‐Edlinger³

2010

Electromagnetics

View full text Add to dashboard Cite

Single-point methods of moment-matching type provide a most effective means for realizing fast frequency sweeps. The impedance formulation of the finite element method is very well-suited for such techniques, but it is susceptible to interior resonances, especially in the case of lossless microwave structures. This deficiency can be resolved by imposing transparent boundary conditions at the waveguide ports, but the resulting matrices exhibit nonpolynomial frequency-dependency unless all waveguide modes are of the transverse electric and magnetic type. In consequence, single-point methods cannot be applied without approximations. This article proposes a fast frequency sweep technique that handles not only transverse electric and magnetic modes but also transverse electric and transverse magnetic modes without any approximations. Moreover, it retains the efficiency of the impedance formulation but prevents interior resonances from occurring. The theoretical background of and numerical evidence for the failure of the impedance formulation is given, and a mathematical proof for the validity of the new method is presented. Computational results demonstrate the reliability and low error of the suggested approach.

show abstract

An Adaptive Multi-Point Fast Frequency Sweep for Large-Scale Finite Element Models

Cited by 23 publications

References 11 publications

A Deterministic-Solution Based Fast Eigenvalue Solver With Guaranteed Convergence for Finite-Element Based 3-D Electromagnetic Analysis

A Deterministic-Solution Based Fast Eigenvalue Solver With Guaranteed Convergence for Finite-Element Based 3-D Electromagnetic Analysis

Adaptive strategies for fast frequency sweeps

Efficient Fast Frequency Sweep Without Nonphysical Resonances

Contact Info

Product

Resources

About