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+34 946 567 842
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+34 946 567 842
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jmunoz@bcamath.org
Information of interest
- Orcid: 0000-0002-1875-8982
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Robust Variational Physics-Informed Neural Networks
Rojas, S.
; Maczuga, P.; Muñoz-Matute, J.; Pardo, D.; Paszynski, M. (2024)
We introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov-Galerkin-type variational formulation of the ...
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An exponential integration generalized multiscale finite element method for parabolic problems
Contreras, L. F.; Pardo, D.; Abreu, E.; Muñoz-Matute, J.; 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.; Pardo, D.; Muga, I.; Muñoz-Matute, J. (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. (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.; 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.; Pardo, D.; 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.; Demkowicz, Leszek; Pardo, D. (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. (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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A DPG-based time-marching scheme for linear hyperbolic problems
Muñoz-Matute, J.; Pardo, D.; 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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Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems
Muñoz-Matute, J.; Pardo, D.; 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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Explicit-in-Time Variational Formulations for Goal-Oriented Adaptivity
Muñoz-Matute, J. (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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Variational Formulations for Explicit Runge-Kutta Methods
Muñoz-Matute, J.; Pardo, D.; Calo, V.M.; Alberdi, E. (2019-08)
Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known ...
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Explicit-in-Time Goal-Oriented Adaptivity
Muñoz-Matute, J.; Calo, V.M.; Pardo, D.; Alberdi, E.; Van der Zee, K.G. (2019-04-15)
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...
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Forward-in-Time Goal-Oriented Adaptivity
Muñoz-Matute, J.; Pardo, D.; Calo, V.M.; Alberdi, E. (2019-03)
In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive ...
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Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
Muñoz-Matute, J.; Alberdi, E.; Pardo, D.; Calo, V.M. (2017-12)
Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the ...