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An exponential integration generalized multiscale finite element method for parabolic problems 

Contreras, L. F.; Pardo, D.Autoridad BCAM; Abreu, E.; Muñoz-Matute, J.Autoridad BCAM; Diaz, C.; Galvis, J. (2023-04-15)
We consider linear and semilinear parabolic problems posed in high-contrast multiscale media in two dimensions. The presence of high-contrast multiscale media adversely affects the accuracy, stability, and overall efficiency ...
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A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks 

Uriarte, C.Autoridad BCAM; Pardo, D.Autoridad BCAM; Muga, I.; Muñoz-Matute, J.Autoridad BCAM (2023-02-15)
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min–max) problem over the ...
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Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of  phi-functions of matrices via quadrature 

Croci, M.; Muñoz-Matute, J.Autoridad BCAM (2023-02-04)
In this article, we propose an algorithm for approximating the action of  $\varphi$-functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with ...
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Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation 

Muñoz-Matute, J.Autoridad BCAM; Demkowicz, L.; Roberts, N. V. (2022-12-01)
In this article, we present a general methodology to combine the Discontinuous Petrov-Galerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We  rst introduce ...
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Exploiting the Kronecker product structure of φ−functions in exponential integrators 

Muñoz-Matute, J.Autoridad BCAM; Pardo, D.Autoridad BCAM; Calo, Victor M. (2022-05-15)
Exponential time integrators are well-established discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ...
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Error representation of the time-marching DPG scheme 

Muñoz-Matute, J.Autoridad BCAM; Demkowicz, Leszek; Pardo, D.Autoridad BCAM (2022-03-01)
In this article, we introduce an error representation function to perform adaptivity in time of the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...
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The DPG Method for the Convection-Reaction Problem, Revisited 

Demkowicz, L.; Roberts, N.V.; Muñoz-Matute, J.Autoridad BCAM (2022-01-01)
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin ...
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Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems 

Muñoz-Matute, J.Autoridad BCAM; Pardo, D.Autoridad BCAM; Demkowicz, L. (2020-11)
The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...
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A DPG-based time-marching scheme for linear hyperbolic problems 

Muñoz-Matute, J.Autoridad BCAM; Pardo, D.Autoridad BCAM; Demkowicz, L. (2020-11)
The Discontinuous Petrov-Galerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...
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Explicit-in-Time Variational Formulations for Goal-Oriented Adaptivity 

Muñoz-Matute, J.Autoridad BCAM (2019-10)
Goal-Oriented Adaptivity (GOA) is a powerful tool to accurately approximate physically relevant features of the solution of Partial Differential Equations (PDEs). It delivers optimal grids to solve challenging engineering ...
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Muñoz-Matute, J. (14)
Pardo, D. (10)Alberdi, E. (4)Calo, V.M. (4)Demkowicz, L. (4)Abreu, E. (1)Calo, Victor M. (1)Contreras, L. F. (1)Croci, M. (1)Demkowicz, Leszek (1)... másSubjectOptimal test functions (4)DPG method (3)Exponential integrators (3)Error representation (2)error representation (2)Finite Element Method (2)goal-oriented adaptivity (2)ODE systems (2)Ultraweak formulation (2)$\varphi$-functions, Kronecker sum, exponential integrators, quadrature rules, scaling and squaring, matrix exponential, Gaussian quadrature, Clenshaw-Curtis quadrature, tensor product structure, semilinear parabolic problems (1)... másFecha2023 (3)2022 (4)2020 (2)2019 (4)2017 (1)

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