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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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thumb|upright=0.5|Optimisation linéaire dans un espace à deux dimensions (x1, x2). La fonction-coût fc est représentée par les lignes de niveau bleues à gauche et par le plan bleu à droite. L'ensemble

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MGT-418: Convex optimization

This course introduces the theory and application of modern convex optimization from an engineering perspective.

ME-271: Fluid flow

Dans ce cours introductif à la physique des fluides, l'étudiant commence par apprendre, au moyen de bilans de masse et de contraintes, à décrire et à prédire les écoulements types. Ces méthodes sont appliquées à des écoulements complexes, tels que les écoulements atmosphériques et tourbillonnaires.

ME-371: Discretization methods in fluids

Ce cours présente une introduction aux méthodes d'approximation utilisées pour la simulation numérique en mécanique des fluides. Les concepts fondamentaux sont présentés dans le cadre de la méthode des différences finies puis étendus à celles des éléments finis et spectraux.

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

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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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Online Modeling For Realtime Facial Animation

Sofien Bouaziz, Mark Pauly

We present a new algorithm for realtime face tracking on commodity RGB-D sensing devices. Our method requires no user-specific training or calibration, or any other form of manual assistance, thus enabling a range of new applications in performance-based facial animation and virtual interaction at the consumer level. The key novelty of our approach is an optimization algorithm that jointly solves for a detailed 3D expression model of the user and the corresponding dynamic tracking parameters. Realtime performance and robust computations are facilitated by a novel subspace parameterization of the dynamic facial expression space. We provide a detailed evaluation that shows that our approach significantly simplifies the performance capture workflow, while achieving accurate facial tracking for realtime applications.

Assoc Computing Machinery2013

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