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A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type. Solver types Types of problems with existing dedicated solvers include:

Linear and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm.
Systems of linear equations.
Nonlinear systems.
Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers.
Linear and non-linear optimisation problems
Systems of ordinary differential equations
Systems of differential algebraic equations
Boolean satisfiability problems, including SAT solvers
Quantified boolean formul

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A Novel Method for the Optimal Parameter Selection of Discrete-Time Switch Model

Chrysanthi Foti, Mario Paolone, Reza Razzaghi

The paper proposes a novel method for the optimal parameter selection of the discrete-time switch model used in circuit solvers that adopt the Fixed Admittance Matrix Nodal Method (FAMNM) approach. As known, FAMNM-based circuit solvers allow to reach efficient computation times since they do not need the inversion of the circuit nodal admittance matrix. However, these solvers need to optimally tune the so-called discrete switch conductance, since this parameter might largely affect the simulations accuracy. Within this context, the method proposed in the paper minimizes the distance between the eigenvalues of the original circuit’s nodal admittance matrix with those associated with the presence of the discrete-time switches. The method is proven to provide values of the discrete-time switch conductance that maximize the simulation accuracy and minimize the losses on this artificial parameter. The performances of the proposed method are finally validated by making reference to two test cases: (i) a circuit composed of RLC elements, (ii) a network model that includes a single-phase transmission line.

The University of British Columbia2013

A Method for the Assessment of the Optimal Parameter of Discrete-Time Switch Model

Chrysanthi Foti, Mario Paolone, Reza Razzaghi

This paper proposes a novel method for the optimal parameter selection of the discrete-time switch model used in circuit solvers that adopt the fixed admittance matrix nodal method (FAMNM) approach. As known, FAMNM-based circuit solvers allow to reach efficient computation times, in particular for real-time simulation applications, since they do not need the inversion of the circuit nodal admittance matrix. However, these solvers need to optimally tune the so-called discrete switch conductance, since this parameter might largely affect the simulations accuracy. Within this context, we propose a method for the determination of the discrete-time switch conductance which is obtained by minimizing the distance between the eigenvalues of the original circuit's nodal admittance matrix with those associated with the circuit including the discrete-time switches. The method is proven to provide values of the discrete-time switch conductance that maximize the simulation accuracy and minimize the losses on this artificially introduced parameter. Additionally, the proposed method avoids the use of trial-and-error process typically required when discrete-time switch conductances need to be addressed in FAMNM approach. The performances of the proposed method are demonstrated for circuits with single and multiple switches in which passive RLC elements and transmission lines are both considered.

Elsevier2014

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