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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: 0000000218758982

Robust Variational PhysicsInformed Neural Networks
(2024)We introduce a Robust version of the Variational PhysicsInformed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a PetrovGalerkintype variational formulation of the ...

An exponential integration generalized multiscale finite element method for parabolic problems
(20230415)We consider linear and semilinear parabolic problems posed in highcontrast multiscale media in two dimensions. The presence of highcontrast multiscale media adversely affects the accuracy, stability, and overall efficiency ...

A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks
(20230215)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 saddlepoint (min–max) problem over the ...

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of phifunctions of matrices via quadrature
(20230204)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 ...

Combining DPG in space with DPG timemarching scheme for the transient advection–reaction equation
(20221201)In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advectionreaction problems. We rst introduce ...

Exploiting the Kronecker product structure of φ−functions in exponential integrators
(20220515)Exponential time integrators are wellestablished discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ...

Error representation of the timemarching DPG scheme
(20220301)In this article, we introduce an error representation function to perform adaptivity in time of the recently developed timemarching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...

The DPG Method for the ConvectionReaction Problem, Revisited
(20220101)We study both conforming and nonconforming versions of the practical DPG method for the convectionreaction problem. We determine that the most common approach for DPG stability analysis  construction of a local Fortin ...

Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems
(202011)The Discontinuous PetrovGalerkin (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 ...

A DPGbased timemarching scheme for linear hyperbolic problems
(202011)The Discontinuous PetrovGalerkin (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 ...

ExplicitinTime Variational Formulations for GoalOriented Adaptivity
(201910)GoalOriented 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 ...

Variational Formulations for Explicit RungeKutta Methods
(201908)Variational spacetime formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop meshadaptive algorithms. Since it is known ...

ExplicitinTime GoalOriented Adaptivity
(20190415)Goaloriented 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 ...

ForwardinTime GoalOriented Adaptivity
(201903)In goaloriented 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 timedependent problems, this adaptive ...

TimeDomain GoalOriented Adaptivity Using PseudoDual Error Representations
(201712)Goaloriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudodual problems for goaloriented adaptivity in the ...