The Experts below are selected from a list of 126126 Experts worldwide ranked by ideXlab platform
Stepan Lucyszyn - One of the best experts on this subject based on the ideXlab platform.
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Computational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity
IEEE Access, 2016Co-Authors: A.a. Muller, Esther Sanabria-codesal, Stepan LucyszynAbstract:Matrix inversion is routinely performed in Computational Engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot-Jacobi (also known as the “Lewis Carol”) identity shows how the determinant of an N+2 order square matrix can be directly computed from the determinants of the N+1 order principal submatrices and N order core submatrix. For the first time, this identity is applied directly to an electrical Engineering problem, simplifying N+2 order coupled matrix filter synthesis (general case, which includes lossy and asymmetrical filters). With the general two-port network theory, we prove the simplification using the Desnanot-Jacobi identity and show that the N+2 coupling matrix can be directly extracted from the zeros of the admittance parameters (given by N+1 order determinants) and poles of the impedance parameters (given by the N order core matrix determinant). The results show that it is possible to decrease the Computational complexity (by eliminating redundancy), reduce the associated cost function (by using less iterations), and under certain circumstances obtain different equivalent solutions. Nevertheless, the method also proves its practical usefulness under constrained optimizations when the user desires specific coupling matrix topologies and constrained coefficient values (e.g, purely real/imaginary/positive/negative). This can lead to a direct coupling matrix constrained configuration where other similar methods fail (using the same optimization algorithms).
A.a. Muller - One of the best experts on this subject based on the ideXlab platform.
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Computational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity
IEEE Access, 2016Co-Authors: A.a. Muller, Esther Sanabria-codesal, Stepan LucyszynAbstract:Matrix inversion is routinely performed in Computational Engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot-Jacobi (also known as the “Lewis Carol”) identity shows how the determinant of an N+2 order square matrix can be directly computed from the determinants of the N+1 order principal submatrices and N order core submatrix. For the first time, this identity is applied directly to an electrical Engineering problem, simplifying N+2 order coupled matrix filter synthesis (general case, which includes lossy and asymmetrical filters). With the general two-port network theory, we prove the simplification using the Desnanot-Jacobi identity and show that the N+2 coupling matrix can be directly extracted from the zeros of the admittance parameters (given by N+1 order determinants) and poles of the impedance parameters (given by the N order core matrix determinant). The results show that it is possible to decrease the Computational complexity (by eliminating redundancy), reduce the associated cost function (by using less iterations), and under certain circumstances obtain different equivalent solutions. Nevertheless, the method also proves its practical usefulness under constrained optimizations when the user desires specific coupling matrix topologies and constrained coefficient values (e.g, purely real/imaginary/positive/negative). This can lead to a direct coupling matrix constrained configuration where other similar methods fail (using the same optimization algorithms).
D Wang - One of the best experts on this subject based on the ideXlab platform.
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accelerating isogeometric boundary element analysis for 3 dimensional elastostatics problems through black box fast multipole method with proper generalized decomposition
International Journal for Numerical Methods in Engineering, 2018Co-Authors: J Trevelyan, W Zhang, D WangAbstract:The isogeometric approach to Computational Engineering analysis makes use of Non-Uniform Rational B-splines (NURBS) to discretise both the geometry and the analysis field variables, giving a higher fidelity geometric description and leading to improved convergence properties of the solution over conventional piecewise polynomial descriptions. Because of its boundary-only modelling, with no requirement for a volumetric NURBS geometric definition, the boundary element method is an ideal choice for isogeometric analysis of solids in 3-D. An isogeometric boundary element analysis (IGABEM) algorithm is presented for the solution of such problems in elasticity, and is accelerated using the black-box Fast Multipole Method (bbFMM). The bbFMM scheme is of O(n) complexity, giving a general kernel-independent separation that can be easily integrated into existing, conventional IGABEM codes with little modification. In the bbFMM scheme, an important process of obtaining a low rank approximation of M2L operators has been hitherto based on Singular Value Decomposition (SVD), which can be very time consuming for large 3-D problems, and this motivates the present work. We introduce the Proper Generalized Decomposition (PGD) method as an alternative approach, and this is demonstrated to enhance efficiency in comparison with schemes that rely on the SVD. In the worst case a factor of approximately 2 performance gain is achieved. Numerical examples show the performance gains that are achievable in comparison to standard IGABEM solutions, and demonstrate that solution accuracy is not affected. The results illustrate the potential of this numerical technique for solving arbitrary large scale elastostatics problems directly from CAD models.
Esther Sanabria-codesal - One of the best experts on this subject based on the ideXlab platform.
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Computational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity
IEEE Access, 2016Co-Authors: A.a. Muller, Esther Sanabria-codesal, Stepan LucyszynAbstract:Matrix inversion is routinely performed in Computational Engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot-Jacobi (also known as the “Lewis Carol”) identity shows how the determinant of an N+2 order square matrix can be directly computed from the determinants of the N+1 order principal submatrices and N order core submatrix. For the first time, this identity is applied directly to an electrical Engineering problem, simplifying N+2 order coupled matrix filter synthesis (general case, which includes lossy and asymmetrical filters). With the general two-port network theory, we prove the simplification using the Desnanot-Jacobi identity and show that the N+2 coupling matrix can be directly extracted from the zeros of the admittance parameters (given by N+1 order determinants) and poles of the impedance parameters (given by the N order core matrix determinant). The results show that it is possible to decrease the Computational complexity (by eliminating redundancy), reduce the associated cost function (by using less iterations), and under certain circumstances obtain different equivalent solutions. Nevertheless, the method also proves its practical usefulness under constrained optimizations when the user desires specific coupling matrix topologies and constrained coefficient values (e.g, purely real/imaginary/positive/negative). This can lead to a direct coupling matrix constrained configuration where other similar methods fail (using the same optimization algorithms).
J Trevelyan - One of the best experts on this subject based on the ideXlab platform.
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accelerating isogeometric boundary element analysis for 3 dimensional elastostatics problems through black box fast multipole method with proper generalized decomposition
International Journal for Numerical Methods in Engineering, 2018Co-Authors: J Trevelyan, W Zhang, D WangAbstract:The isogeometric approach to Computational Engineering analysis makes use of Non-Uniform Rational B-splines (NURBS) to discretise both the geometry and the analysis field variables, giving a higher fidelity geometric description and leading to improved convergence properties of the solution over conventional piecewise polynomial descriptions. Because of its boundary-only modelling, with no requirement for a volumetric NURBS geometric definition, the boundary element method is an ideal choice for isogeometric analysis of solids in 3-D. An isogeometric boundary element analysis (IGABEM) algorithm is presented for the solution of such problems in elasticity, and is accelerated using the black-box Fast Multipole Method (bbFMM). The bbFMM scheme is of O(n) complexity, giving a general kernel-independent separation that can be easily integrated into existing, conventional IGABEM codes with little modification. In the bbFMM scheme, an important process of obtaining a low rank approximation of M2L operators has been hitherto based on Singular Value Decomposition (SVD), which can be very time consuming for large 3-D problems, and this motivates the present work. We introduce the Proper Generalized Decomposition (PGD) method as an alternative approach, and this is demonstrated to enhance efficiency in comparison with schemes that rely on the SVD. In the worst case a factor of approximately 2 performance gain is achieved. Numerical examples show the performance gains that are achievable in comparison to standard IGABEM solutions, and demonstrate that solution accuracy is not affected. The results illustrate the potential of this numerical technique for solving arbitrary large scale elastostatics problems directly from CAD models.