Author
Ignacio Muga
Other affiliations: Valparaiso University, University of Texas at Austin
Bio: Ignacio Muga is an academic researcher from Pontifical Catholic University of Valparaíso. The author has contributed to research in topics: Finite element method & Residual. The author has an hindex of 12, co-authored 36 publications receiving 477 citations. Previous affiliations of Ignacio Muga include Valparaiso University & University of Texas at Austin.
Papers
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TL;DR: This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case.
138 citations
TL;DR: In this article, a discontinuous Petrov Galerkin (DPG) method for acoustic wave propagation has been proposed, which yields Hermitian positive definite matrices and has good pre-asymptotic stability properties.
98 citations
TL;DR: This paper studies the discontinuous Petrov--Galerkin (DPG) method, where the test space is normed by a modified graph norm, and the modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter.
Abstract: This paper studies the discontinuous Petrov--Galerkin (DPG) method, where the test space is normed by a modified graph norm The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter The main finding is that as the parameter approaches zero, better results are obtained, under some circumstances, when the method is applied to the Helmholtz equation The main tool used is a dispersion analysis on the multiple interacting stencils that form the DPG method The analysis shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the computed wave approximations Since the DPG method is a nonstandard least-squares Galerkin method, its performance is compared with a standard least-squares method having a similar stencil
36 citations
TL;DR: Duran et al. as mentioned in this paper obtained uniqueness and existence results of an outgoing solution for the Helmholtz equation in a half-space, or in a compact local perturbation of it, with an impedance boundary condition.
Abstract: We obtain uniqueness and existence results of an outgoing solution for the Helmholtz equation in a half-space, or in a compact local perturbation of it, with an impedance boundary condition. It is worth noting that these kinds of domains have unbounded boundaries which lead to a non-classical exterior problem. The established radiation condition is somewhat different from the usual Sommerfeld’s one, due to the appearance of surface waves (in the case of a non-absorbing boundary). A half-space Green’s function framework is used to carry out our computations. This is an extended and detailed version of the previous article “The Helmholtz equation with impedance in a half-space,” Duran et al. (CR Acad Sci Paris Ser I 341:561–566, 2005).
28 citations
TL;DR: In this article, a new adaptive stabilized finite element method is proposed to construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that has infsup stability.
24 citations
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Journal Article•
28,685 citations
Journal Article•
1,019 citations
01 Jan 2016
TL;DR: The nonlinear functional analysis and its applications is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
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581 citations