The Experts below are selected from a list of 264 Experts worldwide ranked by ideXlab platform

Ayse Kiper - One of the best experts on this subject based on the ideXlab platform.

S. Vergura - One of the best experts on this subject based on the ideXlab platform.

  • The Gauss Elimination from the circuit theory point of view: Diagonal nodal equivalent
    IEEE EUROCON 2009, 2009
    Co-Authors: S. Vergura
    Abstract:

    Nodal analysis is known to be the most used method to write the solving equations of electrical circuits. The matrix equation is usually solved by using Gauss Elimination (GE). This paper studies in depth the GE from a circuit theory point of view. It results that each step of GE constitutes a modification of the assigned circuit. The forward Elimination can be considered as a successive removal of the independent nodes by introducing voltage-controlled current sources, while back substitution leads to independent elementary circuits. The whole procedure can be systematically applied; in this way, given a circuit, it is possible to switch to a modified circuit, by means of circuital transformations corresponding to mathematical ones. Similar approach can be used also when the mesh analysis is used to solve a circuit. In this case the forward Elimination can be considered as a successive removal of the independent meshes by introducing current-controlled voltage sources.

  • the Gauss Elimination from the circuit theory point of view diagonal nodal equivalent
    IEEE EUROCON, 2009
    Co-Authors: S. Vergura
    Abstract:

    Nodal analysis is known to be the most used method to write the solving equations of electrical circuits. The matrix equation is usually solved by using Gauss Elimination (GE). This paper studies in depth the GE from a circuit theory point of view. It results that each step of GE constitutes a modification of the assigned circuit. The forward Elimination can be considered as a successive removal of the independent nodes by introducing voltage-controlled current sources, while back substitution leads to independent elementary circuits. The whole procedure can be systematically applied; in this way, given a circuit, it is possible to switch to a modified circuit, by means of circuital transformations corresponding to mathematical ones. Similar approach can be used also when the mesh analysis is used to solve a circuit. In this case the forward Elimination can be considered as a successive removal of the independent meshes by introducing current-controlled voltage sources.

  • The Gauss Elimination from the Circuit Theory Point of View: Triangular Mesh Equivalent
    EUROCON 2005 - The International Conference on "Computer as a Tool", 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    A method utilized to solve large electric network is the mesh analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit theory point of view. It results that GE represents a modification of the assigned circuit. These modifications can be considered as successive removals of the meshes. The whole procedure can be systematically interpreted; in this way, after a circuit is assigned, it is possible to switch to a modified circuit, considering circuital transformations in role of mathematical ones

  • The Gauss Elimination from the Circuit Theory Point of View: Triangular Nodal Equivalent
    EUROCON 2005 - The International Conference on "Computer as a Tool", 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    The most used method utilized to solve an electric network is the nodal analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit point of view. It results that GE represents a modification of the assigned circuit. Such a modification can be considered as a successive removal of independent nodes. The whole procedure can be systematically applied; in this way, given a circuit, it is possible to switch to a modified circuit, by means of circuit transformations corresponding to mathematical ones

  • the Gauss Elimination from the circuit theory point of view triangular nodal equivalent
    Conference on Computer as a Tool, 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    A method utilized to solve large electric network is the mesh analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit theory point of view. It results that GE represents a modification of the assigned circuit. These modifications can be considered as successive removals of the meshes. The whole procedure can be systematically interpreted; in this way, after a circuit is assigned, it is possible to switch to a modified circuit, considering circuital transformations in role of mathematical ones

John R Rice - One of the best experts on this subject based on the ideXlab platform.

  • an organization of sparse Gauss Elimination for solving partial differntial equations on distributed memory machines
    Numerical Methods for Partial Differential Equations, 1993
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    A computational arrangement of Gauss Elimination is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation problems. It is particularly targeted for use on distributed memory message passing multiprocessor computers and it is presented and analyzed in this context. The objective of the algorithm is to exploit the sparsity (i.e., reducing computation, communication, and memory requirements) and to optimize the data structure manipulation overhead. The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single, nearly dense system at the last stage. The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different. Thus we use different types of data structures and algorithm components at different stages of the solution. The new organization is a combination of previous techniques including nested dissection, implicit block factorization, domain decomposition, fan-in, fan-out, up-looking, down-looking, and dynamic data structures. © 1993 John Wiley & Sons, Inc.

  • row oriented Gauss Elimination on distributed memory multiprocessors
    International Journal of High Speed Computing, 1992
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    This paper deals with the Gauss Elimination for solving general dense linear systems on distributed memory multiprocessors. A row oriented parallel algorithm is proposed and implemented on the NCUBE distributed memory multiprocessor. We study in some detail various implementation choices which are important factors affecting the algorithm's performance. These factors include: mapping of rows into processors, pivoting implementation, message passing, communication granularity and pipelining. Experiments with these on the NCUBE are reported which illustrate the algorithms performance characteristics. Both standard and memory scaled speed up are measured which show that the algorithm is very efficient. Comparisons with previous approaches which mix row and column operations show an obvious gain in efficiency.

  • a new organization of sparse Gauss Elimination for solving pdes
    1990
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    A new Gauss Elimination algorithm is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation (PDE) problems. It is particularly suitable for use on distributed memory message passing (DMMP) multiprocessor computers and it is presented and analyzed in this context. The objective of the algorithm is to exploit the sparsity (Le., reducing both computational and memory requirements) and sharply reduce the data structure manipulation overhead of standard sparse matrix algorithms. The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single. nearly dense system at the last stage. The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different. Thus we use different types of data structures and algorithm components at different stages of the solution. .. Supported by NSF grant CCR-8619817. ..... Supported in part by AFOSR grant 88-0243 and the Strategic Defense Initiative through ARO conlnlCl DAAG03-86-K-OI06. L INTRODUCTION Solving linear PDEs naturally generates large, sparse linear systems of equations to solve. These systems have structures which are not exploited by general purpose sparse matrix algorithms and we present a new organization of sparse Gauss Elimination tailored to e;qIloit-these structures. We stan with some general background comments on sparse rnattix melhods for PDE problems. The linear systems are almost always created by the PDE solving system with the equations (manix rows) distributed among the processors. One has the freedom to choose the assignment of rows to processors, but one cannot choose to have columns assigned to processors wiilieut the high expense of performing a matrix transpose (or equivalent) on a DMMP machine. The linear systems are conunonly non-symmetric so that a solver of symmetric systems is applicable to a limited class of PDE problems and/or discretization methods. The lack of symmetry requires two data srructures on a DMMP machine, one each for the row and column sparsities. One can combine these in clever ways, but it is prohibitedly expensive to repeatedly obtain column sparsity information from the row sparsity structure. Note that similar sparsity patterns occur in other imponant applications (e.g., least squares problems [Rice, 1984]) and the considerations studied here for PDE problems are also relevant there. Symbolic factorization is not well suited for non-symmetric systems as. so far, the techniques generate much too large a data structure. Merging the symbolic factorization with the numerical computation is not inherently more expensive than doing these separately and, for non-symmetric systems, it allows the final data structure to be just the required size for the system. This dynamic data structure creation is used in the parallel sparse algorithm of [Mu and Rice, 1990.]. If nested dissection is performed geometrically rather than algebraically (as is natural in PDE problems), then a great deal of matrix structure is known "a priori" from the geometric structure and need not be explicitly expressed in the sparse matrix data structure. This idea is exploited in parallel sparse [Mu and Rice, 1989a] to some extent. There are two general row oriented organizations of Gauss Elimination focusing on what happens when one eliminates an unknown from a pivot equation. Theyare/an·in and fan~our schemes. Another imponant organization is the mulrlfrontal scheme which is unknown oriented (using both rows and columns associated with unknowns). The fan-in organization processes the LV factorization row by row as follows.

F. Vacca - One of the best experts on this subject based on the ideXlab platform.

  • The Gauss Elimination from the Circuit Theory Point of View: Triangular Mesh Equivalent
    EUROCON 2005 - The International Conference on "Computer as a Tool", 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    A method utilized to solve large electric network is the mesh analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit theory point of view. It results that GE represents a modification of the assigned circuit. These modifications can be considered as successive removals of the meshes. The whole procedure can be systematically interpreted; in this way, after a circuit is assigned, it is possible to switch to a modified circuit, considering circuital transformations in role of mathematical ones

  • The Gauss Elimination from the Circuit Theory Point of View: Triangular Nodal Equivalent
    EUROCON 2005 - The International Conference on "Computer as a Tool", 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    The most used method utilized to solve an electric network is the nodal analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit point of view. It results that GE represents a modification of the assigned circuit. Such a modification can be considered as a successive removal of independent nodes. The whole procedure can be systematically applied; in this way, given a circuit, it is possible to switch to a modified circuit, by means of circuit transformations corresponding to mathematical ones

  • the Gauss Elimination from the circuit theory point of view triangular nodal equivalent
    Conference on Computer as a Tool, 2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    A method utilized to solve large electric network is the mesh analysis. After obtaining the matrix equation it can be solved by using Gauss Elimination (GE). This paper analyzes the GE from a circuit theory point of view. It results that GE represents a modification of the assigned circuit. These modifications can be considered as successive removals of the meshes. The whole procedure can be systematically interpreted; in this way, after a circuit is assigned, it is possible to switch to a modified circuit, considering circuital transformations in role of mathematical ones

  • the Gauss Elimination from thecircuit theory pointofview triangularmesh equivalent
    2005
    Co-Authors: F. Vacca, S. Vergura
    Abstract:

    A methodutilized tosolvelargeelectric networkisthemeshanalysis. Afterobtaining thematrix equation itcanbesolved byusingGaussElimination (GE). Thispaperanalyzes theGE froma circuit theory pointof view.Itresults thatGE represents a modification ofthe assigned circuit. Thesemodifications canbeconsidered as successive removals ofthemeshes. Thewholeprocedure canbesystematically interpreted; in this way,after acircuit isassigned, itispossible toswitch toa modified circuit, considering circuital transformations inrole ofmathematical ones.

Mo Mu - One of the best experts on this subject based on the ideXlab platform.

  • an organization of sparse Gauss Elimination for solving partial differntial equations on distributed memory machines
    Numerical Methods for Partial Differential Equations, 1993
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    A computational arrangement of Gauss Elimination is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation problems. It is particularly targeted for use on distributed memory message passing multiprocessor computers and it is presented and analyzed in this context. The objective of the algorithm is to exploit the sparsity (i.e., reducing computation, communication, and memory requirements) and to optimize the data structure manipulation overhead. The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single, nearly dense system at the last stage. The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different. Thus we use different types of data structures and algorithm components at different stages of the solution. The new organization is a combination of previous techniques including nested dissection, implicit block factorization, domain decomposition, fan-in, fan-out, up-looking, down-looking, and dynamic data structures. © 1993 John Wiley & Sons, Inc.

  • row oriented Gauss Elimination on distributed memory multiprocessors
    International Journal of High Speed Computing, 1992
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    This paper deals with the Gauss Elimination for solving general dense linear systems on distributed memory multiprocessors. A row oriented parallel algorithm is proposed and implemented on the NCUBE distributed memory multiprocessor. We study in some detail various implementation choices which are important factors affecting the algorithm's performance. These factors include: mapping of rows into processors, pivoting implementation, message passing, communication granularity and pipelining. Experiments with these on the NCUBE are reported which illustrate the algorithms performance characteristics. Both standard and memory scaled speed up are measured which show that the algorithm is very efficient. Comparisons with previous approaches which mix row and column operations show an obvious gain in efficiency.

  • a new organization of sparse Gauss Elimination for solving pdes
    1990
    Co-Authors: Mo Mu, John R Rice
    Abstract:

    A new Gauss Elimination algorithm is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation (PDE) problems. It is particularly suitable for use on distributed memory message passing (DMMP) multiprocessor computers and it is presented and analyzed in this context. The objective of the algorithm is to exploit the sparsity (Le., reducing both computational and memory requirements) and sharply reduce the data structure manipulation overhead of standard sparse matrix algorithms. The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single. nearly dense system at the last stage. The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different. Thus we use different types of data structures and algorithm components at different stages of the solution. .. Supported by NSF grant CCR-8619817. ..... Supported in part by AFOSR grant 88-0243 and the Strategic Defense Initiative through ARO conlnlCl DAAG03-86-K-OI06. L INTRODUCTION Solving linear PDEs naturally generates large, sparse linear systems of equations to solve. These systems have structures which are not exploited by general purpose sparse matrix algorithms and we present a new organization of sparse Gauss Elimination tailored to e;qIloit-these structures. We stan with some general background comments on sparse rnattix melhods for PDE problems. The linear systems are almost always created by the PDE solving system with the equations (manix rows) distributed among the processors. One has the freedom to choose the assignment of rows to processors, but one cannot choose to have columns assigned to processors wiilieut the high expense of performing a matrix transpose (or equivalent) on a DMMP machine. The linear systems are conunonly non-symmetric so that a solver of symmetric systems is applicable to a limited class of PDE problems and/or discretization methods. The lack of symmetry requires two data srructures on a DMMP machine, one each for the row and column sparsities. One can combine these in clever ways, but it is prohibitedly expensive to repeatedly obtain column sparsity information from the row sparsity structure. Note that similar sparsity patterns occur in other imponant applications (e.g., least squares problems [Rice, 1984]) and the considerations studied here for PDE problems are also relevant there. Symbolic factorization is not well suited for non-symmetric systems as. so far, the techniques generate much too large a data structure. Merging the symbolic factorization with the numerical computation is not inherently more expensive than doing these separately and, for non-symmetric systems, it allows the final data structure to be just the required size for the system. This dynamic data structure creation is used in the parallel sparse algorithm of [Mu and Rice, 1990.]. If nested dissection is performed geometrically rather than algebraically (as is natural in PDE problems), then a great deal of matrix structure is known "a priori" from the geometric structure and need not be explicitly expressed in the sparse matrix data structure. This idea is exploited in parallel sparse [Mu and Rice, 1989a] to some extent. There are two general row oriented organizations of Gauss Elimination focusing on what happens when one eliminates an unknown from a pivot equation. Theyare/an·in and fan~our schemes. Another imponant organization is the mulrlfrontal scheme which is unknown oriented (using both rows and columns associated with unknowns). The fan-in organization processes the LV factorization row by row as follows.