The Experts below are selected from a list of 122814 Experts worldwide ranked by ideXlab platform
Jianming Jin - One of the best experts on this subject based on the ideXlab platform.
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application of the tree cotree splitting for improving matrix conditioning in the full wave finite element analysis of high speed circuits
IEEE Antennas and Propagation Society International Symposium, 2008Co-Authors: Shihhao Lee, Jianming JinAbstract:In recent years the development of high-speed circuits leads to a demand in accurate and reliable full-wave electromagnetic analysis from high frequencies all the way to DC, and thus brings a challenge to current full-wave techniques. A full-wave solver yields solutions with deteriorated accuracy or even breakdowns at low frequencies due to Ill-Conditioned System matrices. The same situation also happens when very small elements (compared to the wavelength) exist in the finite-element discretization, which is similar to a low-frequency case [1]. This is actually very common in circuit problems since there are very dense meshes both inside and outside conductors for modeling the conductor loss and the field singularity, respectively. In this case an element may not only be very small, but also have a high aspect ratio, which make a System matrix very Ill-Conditioned even at not too low frequencies.
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application of the tree cotree splitting for improving matrix conditioning in the full wave finite element analysis of high speed circuits
Microwave and Optical Technology Letters, 2008Co-Authors: Shihhao Lee, Jianming JinAbstract:In this study the tree-cotree splitting technique is applied for improving the finite-element matrix conditioning for the analysis of high-speed circuits. A well-known issue is that at low frequencies a full-wave solver yields less accurate solutions and may even breakdown due to Ill-Conditioned System matrices. To enhance the capability and reliability of the conventional finite element method in broadband full-wave analyses, we apply the tree-cotree splitting to edge elements to account for the decoupling between the electric and magnetic fields at low frequencies, which is the main reason for the low-frequency problem. The algorithm for finding a minimum spanning tree when there exist wave ports, lumped ports, or for a PEC-free structure are described. Besides, a model order reduction method, called the solution space projection, is applied for a fast broadband analysis. We further propose an expansion to available solution bases for a better approximation to low-frequency fields, so that a simulation can be extended to extremely low frequencies. The application is focused on the simulation of high-speed circuits, of which both low and high frequency characteristics are of equal importance. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1476–1481, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23403
Kurt Maute - One of the best experts on this subject based on the ideXlab platform.
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A simple and efficient preconditioning scheme for heaviside enriched XFEM
Computational Mechanics, 2014Co-Authors: Christapher Lang, David Makhija, Alireza Doostan, Kurt MauteAbstract:The extended finite element method (XFEM) is an approach for solving problems with non-smooth solutions, which arise from geometric features such as cracks, holes, and material inclusions. In the XFEM, the approximate solution is locally enriched to capture the discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an Ill-Conditioned System of equations results when the ratio of volumes on either side of the interface in an element is small. Such interface configurations are often unavoidable, in particular for moving interface problems on fixed meshes. In general, the ill-conditioning reduces the performance of iterative linear solvers and impedes the convergence of solvers for nonlinear problems. This paper studies the XFEM with a Heaviside enrichment strategy for solving problems with stationary and moving material interfaces. A generalized formulation of the XFEM is combined with the level set method to implicitly define the embedded interface geometry. In order to avoid the ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. The geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the System of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces. It is shown by numerical examples that the proposed preconditioning scheme performs well for discontinuous problems and $$C^0$$ C 0 -continuous problems with both the stabilized Lagrange and Nitsche methods for enforcing the continuity constraint at the interface. Numerical examples are presented which compare the condition number and solution error with and without the proposed preconditioning scheme. The results suggest that the proposed preconditioning scheme leads to condition numbers similar to that of a body-fitted mesh using the traditional finite element method without loss of solution accuracy.
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a simple and efficient preconditioning scheme for heaviside enriched xfem
arXiv: Numerical Analysis, 2013Co-Authors: Christapher Lang, David Makhija, Alireza Doostan, Kurt MauteAbstract:The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an Ill-Conditioned System of equations results when the ratio of volumes on either side of the interface in an element is small. In this paper, to avoid this ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. This geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the System of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces.
Shihhao Lee - One of the best experts on this subject based on the ideXlab platform.
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application of the tree cotree splitting for improving matrix conditioning in the full wave finite element analysis of high speed circuits
IEEE Antennas and Propagation Society International Symposium, 2008Co-Authors: Shihhao Lee, Jianming JinAbstract:In recent years the development of high-speed circuits leads to a demand in accurate and reliable full-wave electromagnetic analysis from high frequencies all the way to DC, and thus brings a challenge to current full-wave techniques. A full-wave solver yields solutions with deteriorated accuracy or even breakdowns at low frequencies due to Ill-Conditioned System matrices. The same situation also happens when very small elements (compared to the wavelength) exist in the finite-element discretization, which is similar to a low-frequency case [1]. This is actually very common in circuit problems since there are very dense meshes both inside and outside conductors for modeling the conductor loss and the field singularity, respectively. In this case an element may not only be very small, but also have a high aspect ratio, which make a System matrix very Ill-Conditioned even at not too low frequencies.
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application of the tree cotree splitting for improving matrix conditioning in the full wave finite element analysis of high speed circuits
Microwave and Optical Technology Letters, 2008Co-Authors: Shihhao Lee, Jianming JinAbstract:In this study the tree-cotree splitting technique is applied for improving the finite-element matrix conditioning for the analysis of high-speed circuits. A well-known issue is that at low frequencies a full-wave solver yields less accurate solutions and may even breakdown due to Ill-Conditioned System matrices. To enhance the capability and reliability of the conventional finite element method in broadband full-wave analyses, we apply the tree-cotree splitting to edge elements to account for the decoupling between the electric and magnetic fields at low frequencies, which is the main reason for the low-frequency problem. The algorithm for finding a minimum spanning tree when there exist wave ports, lumped ports, or for a PEC-free structure are described. Besides, a model order reduction method, called the solution space projection, is applied for a fast broadband analysis. We further propose an expansion to available solution bases for a better approximation to low-frequency fields, so that a simulation can be extended to extremely low frequencies. The application is focused on the simulation of high-speed circuits, of which both low and high frequency characteristics are of equal importance. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1476–1481, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23403
Christapher Lang - One of the best experts on this subject based on the ideXlab platform.
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A simple and efficient preconditioning scheme for heaviside enriched XFEM
Computational Mechanics, 2014Co-Authors: Christapher Lang, David Makhija, Alireza Doostan, Kurt MauteAbstract:The extended finite element method (XFEM) is an approach for solving problems with non-smooth solutions, which arise from geometric features such as cracks, holes, and material inclusions. In the XFEM, the approximate solution is locally enriched to capture the discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an Ill-Conditioned System of equations results when the ratio of volumes on either side of the interface in an element is small. Such interface configurations are often unavoidable, in particular for moving interface problems on fixed meshes. In general, the ill-conditioning reduces the performance of iterative linear solvers and impedes the convergence of solvers for nonlinear problems. This paper studies the XFEM with a Heaviside enrichment strategy for solving problems with stationary and moving material interfaces. A generalized formulation of the XFEM is combined with the level set method to implicitly define the embedded interface geometry. In order to avoid the ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. The geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the System of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces. It is shown by numerical examples that the proposed preconditioning scheme performs well for discontinuous problems and $$C^0$$ C 0 -continuous problems with both the stabilized Lagrange and Nitsche methods for enforcing the continuity constraint at the interface. Numerical examples are presented which compare the condition number and solution error with and without the proposed preconditioning scheme. The results suggest that the proposed preconditioning scheme leads to condition numbers similar to that of a body-fitted mesh using the traditional finite element method without loss of solution accuracy.
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a simple and efficient preconditioning scheme for heaviside enriched xfem
arXiv: Numerical Analysis, 2013Co-Authors: Christapher Lang, David Makhija, Alireza Doostan, Kurt MauteAbstract:The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an Ill-Conditioned System of equations results when the ratio of volumes on either side of the interface in an element is small. In this paper, to avoid this ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. This geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the System of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces.
Felicio Bruzzi Barros - One of the best experts on this subject based on the ideXlab platform.
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well conditioning global local analysis using stable generalized extended finite element method for linear elastic fracture mechanics
Computational Mechanics, 2016Co-Authors: Mohammad Malekan, Felicio Bruzzi BarrosAbstract:Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning System of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global---local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global---local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global---local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global---local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global---local enrichments lead to Ill-Conditioned System matrices and bad convergence rate.
