Grzegorz Fotyga

Efficient Model Order Reduction for FEM Analysis of Waveguide Structures and Resonators

An e-cient model order reduction method for three- dimensional Finite Element Method (FEM) analysis of waveguide structures is proposed. The method is based on the E-cient Modal Order Reduction (ENOR) algorithm for creating macro-elements in cascaded subdomains. The resulting macro-elements are represented by very compact submatrices, leading to signiflcant reduction of the overall number of unknowns. The e-ciency of the model order reduction is enhanced by projecting flelds at the boundaries of macro- elements onto a subspace spanned by a few low-order waveguide modes. The combination of these two techniques results in considerable saving in overall computational time and memory requirement. An additional advantage of the presented method is that the reduced- order system matrix remains frequency-independent, which allows for very fast frequency sweeping and e-cient calculation of resonant frequencies. Several numerical examples for driven and eigenvalue problems demonstrate the performance of the proposed methodology in terms of accuracy, memory usage and simulation time.

Automated Reduced Model Order Selection

This letter proposes to automate generation of reduced-order models used for accelerated S-parameter computation by applying a posteriori model error estimators. So far, a posteriori error estimators were used in Reduced Basis Method (RBM) and Proper Orthogonal Decomposition (POD) to select frequency points at which basis vectors are generated. This letter shows how a posteriori error estimators can be applied to automatically select the order of the reduced model in second-order Model Order Reduction (MOR) methods. Three different error estimators are investigated and compared in order to arrive at a new MOR scheme that is fast, reliable, and fully automated. The effectiveness of the proposed approach is verified by very high accuracy of the computed scattering parameters ( S-parameters) for an example of a waveguide filter over a prescribed frequency band.

A New Type of Macro-Elements for Efficient Two-Dimensional FEM Analysis

This letter deals with a model order reduction technique applicable for driven and eigenvalue problems solved using the finite element method (FEM). It allows one to efficiently compute electromagnetic parameters of structures comprising small features that require strong local mesh refinement. The subdomains of very fine mesh are separated from the global domain as so called macro-elements that undergo model reduction. The macro-elements of reduced order are described by a significantly smaller number of unknowns, thus improving overall simulation speed. In addition, we present an algorithm of macro-elements multiple reuse, called cloning, which provides further decrease of the computation time and memory requirements. The results of the two numerical experiments, in which the local mesh refinement exceeds the factor of 400, illustrate the properties of the proposed methodology and prove that it increases the FEM efficiency significantly and is particularly suitable for multiscale problems with strong variations of desired mesh density.

Wideband Macromodels in Finite Element Method

This letter proposes a novel projection technique for accelerating Finite Element Method simulations. The algorithm is based on the Second-order Arnoldi Method for Passive Order Reduction (SAPOR). It involves generation of two projection bases and thanks to this it is applicable to the systems of equations, which contain the quadratic frequency-dependence in the input term, that arise when projection is applied locally in the selected subregions of the computational domain. Numerical experiments show, that the proposed approach can be used to generate local macromodels, which are reliable for the wide frequency band simulations.

A 3D-FEM mesh technique for fast analysis of waveguide problems containing rotatable tuning elements

In this paper a meshing technique for 3D Finite Element Method is presented. It allows for fast analysis and optimization of the waveguide structures, which contain rotatable tuning elements. In the proposed procedure a thin layer of varying cylindrical mesh buffer is introduced in order to reuse unchanged mesh and FEM matrices in the rest of the domain.

Local mesh morphing technique for parametrized macromodels in the finite element method

This paper presents a novel approach for enhancing the efficiency of the design process of microwave devices by means of the finite element method. It combines mesh morphing with local model order reduction (MOR) and yields parametrized macromodels that can be used to significantly reduce the number of variables in the FEM system of equations and acceleration of computer simulation. A projection basis for local reduction is generated only once, for the original geometry and the associated mesh. The projection basis generated for the nominal design is subsequently used for updated geometries and morphed meshes thereby allowing for reducing the numerical cost and the computational time of parametric studies or the optimization process. The performance of the proposed approach is demonstrated on a two dimensional example.

Wideband Model Order reduction for macromodels in Finite Element Method

This paper presents a novel algorithm for accelerating 3D Finite Element Method simulations by introducing macromodels created in local model order reduction in the selected subdomains of the computational domain. It generates the projection basis for a compact system of equations associated with a separate subdomain. Due to non-linear frequency dependency in the Right Hand Side (RHS), the standard reduction methods do not perform properly. The proposed algorithm alleviates this problem being easy to implement and accurate in wide frequency band simulations of complex structures.

Reduced order modelling of microwave components by means of higher-order finite-element method

The paper addresses several problems related to automated construction of reduced order models that are used to achieve very fast fast frequency sweeps in full-wave simulations of microwave components by means of finite-element method. Four error estimators are presented and examined. Also the correlation between models constructed from FEM matrices of various size, obtained using higher-order basis functions in FEM, is investigated, as well as the impact of the choice of the expansion point on the distribution of error in the simulation band. The findings of this study provide useful guidelines for developing fast FEM code with wideband frequency sweeps acceleration.

Reduced order models in computational electromagnetics (in memory of Ruediger Vahldieck)

This paper reviews research of Ruediger Vahldiecks group and the group at the Gdansk University of Technology in the area of model order reduction techniques for accelerating full-wave simulations. The applications of reduced order models to filter design as well as of local and nested (multilevel) macromodels for solving 3D wave equations and wave-guiding problems using finite difference and finite element methods are discussed.

Local Mesh Deformation for accelerated parametric studies based on the Finite Element Method

This paper presents an approach for enhancing the efficiency of two-dimensional Finite Element Method analysis in parametric studies or optimisation process of microwave components. The new approach involves local mesh deformation applied near the elements that are modified during computations. Since in the proposed approach the topology of the mesh remains unchanged, a new mesh does not have to be generated from scratch when the geometry changes. In effect, substantial reduction of time taken by parametric studies or optimization of microwave components can be achieved, especially if the technique is combined with local Model-Order Reduction, called macromodeling.