Browsing by Author "Gatica, Gabriel N."
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- ItemA DIRECT COUPLING OF LOCAL DISCONTINUOUS GALERKIN AND BOUNDARY ELEMENT METHODS(2010) Gatica, Gabriel N.; Heuer, Norbert; Javier Sayas, FranciscoThe coupling of local discontinuous Galerkin (LDG) and boundary element methods (BEM), which has been developed recently to solve linear and nonlinear exterior transmission problems, employs a mortar-type auxiliary unknown to deal with the weak continuity of the traces at the interface boundary. As a consequence, the main features of LDG and BEM are maintained and hence the coupled approach benefits from the advantages of both methods. In this paper we propose and analyze a simplified procedure that avoids the mortar variable by employing LDG subspaces whose functions are continuous on the coupling boundary. The continuity can be implemented either directly or indirectly via the use of Lagrangian multipliers. In this way, the normal derivative becomes the only boundary unknown, and hence the total number of unknown functions is reduced by two. We prove the stability of the new discrete scheme and derive an a priori error estimate in the energy norm. A numerical example confirming the theoretical result is provided. The analysis is also extended to the case of nonlinear problems and to the coupling with other discontinuous Galerkin methods.
- ItemA direct coupling of local discontinuous Galerkin and bounsary element methods(2010) Gatica, Gabriel N.; Heuer, Norbert; Sayas, Francisco Javier
- ItemA dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity(2000) Gatica, Gabriel N.; Heuer, Norbert
- ItemA posteriori error estimates for a mixed-FEM formulation of a non-linear elliptic problem(2002) Araya, Rodolfo; Barrios, Tomás P.; Gatica, Gabriel N.; Heuer, Norbert
- ItemA preconditioned MINRES method for the coupling of mixed-FEM and BEM for some nonlinear problems(2002) Gatica, Gabriel N.; Heuer, Norbert
- ItemA priori and a posteriori error analysis of an augmented mixed finite element method for incompressible fluid flows(2008) Figueroa, Leonardo E.; Gatica, Gabriel N.; Heuer, Norbert
- ItemA residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity(2006) Barrios, Tomás P.; Gatica, Gabriel N.; González, María; Heuer, Norbert
- ItemAdaptive Mesh Refinement in Deformable Image Registration: A Posteriori Error Estimates for Primal and Mixed Formulations(2021) Barnafi, Nicolas; Gatica, Gabriel N.; Hurtado, Daniel E.; Miranda, Willian; Ruiz-Baier, RicardoDeformable image registration (DIR) is a popular technique for the alignment of digital images, with highly relevant applications in medical image analysis. However, the numerical solution of DIR problems can be very challenging in computational terms, as the improvement of the DIR solution typically involves a uniform refinement of the underlying domain discretization that exponentially increases the number of degrees of freedom. In this work, we develop adaptive mesh refinement schemes particularly designed for the finite-element solution of DIR problems. We start by deriving residual-based a posteriori error estimators for the primal and mixed formulations of the DIR problem and show that they are reliable and efficient. Based on these error estimators, we implement adaptive mesh-refinement schemes into a finite-element code to register images. We assess the numerical performance of the proposed adaptive scheme on smooth synthetic images, where numerical convergence is verified. We further show that the adaptive mesh refinement scheme can deliver solutions to DIR problems with significant reductions in the number of degrees of freedom without compromising the accuracy of the solution. We also confirm that the adaptive scheme proposed for the mixed DIR formulation successfully handles volume-constrained registration problems, providing optimal convergence in analytic examples. To demonstrate the applicability of the method, we perform adaptive DIR on medical brain images and binary images and study how image noise affects the proposed refinement schemes.
- ItemAn a posteriori error estimate for a linear-nonlinear transmission problem in plane elastostatics(2002) Barrientos, Mauricio A.; Gatica, Gabriel N.; Heuer, Norbert
- ItemAn expanded mixed finite element approach via a dual-dual formulation and the minimum residual method(2001) Gatica, Gabriel N.; Heuer, Norbert
- ItemAn implicit-explicit residual error estimator for the coupling of dual-mixed finite elements and boundary elements in elastostatics(2001) Gatica, Gabriel N.; Heuer, Norbert; Stephan, Ernst P.
- ItemConjugate gradient method for dual-dual mixed formulations(2002) Gatica, Gabriel N.; Heuer, Norbert
- ItemCoupling of mixed finite element and stabilized boundary element methods for a fluid-solid interaction problem in 3D(2014) Gatica, Gabriel N.; Heuer, Norbert; Meddahi, S.
- ItemLinear Control applied to a non-isolated bidirectional DC-DC converter with Interleave technique powered by variable sources(IEEE, 2019) Salgado, J.; Rojas, F.; Pereda Torres, Javier Eduardo; Díaz, M.; Gatica, Gabriel N.In this article, a linear control strategy is presented applied to a Synchronous Buck converter, which allows N sub-converters to operate in parallel, operating in Interleave mode, balancing the currents in each of the sub-converters and maintaining their dynamic response invariant over a wide range of operation, even when their DC links vary as it would be in a system with electric batteries. Simulation results validating this behavior, using variable DC sources are presented and discussed in this article.
- ItemMinimum residual iteration for a dual-dual mixed formulation of exterior transmission problems(2001) Gatica, Gabriel N.; Heuer, Norbert
- ItemNew primal and dual-mixed finite element methods for stable image registration with singular regularization(2021) Barnafi, Nicolas; Gatica, Gabriel N.; Hurtado, Daniel E.; Miranda, Willian; Ruiz-Baier, RicardoThis work introduces and analyzes new primal and dual-mixed finite element methods for deformable image registration, in which the regularizer has a nontrivial kernel, and constructed under minimal assumptions of the registration model: Lipschitz continuity of the similarity measure and ellipticity of the regularizer on the orthogonal complement of its kernel. The aforementioned singularity of the regularizer suggests to modify the original model by incorporating the additional degrees of freedom arising from its kernel, thus granting ellipticity of the former on the whole solution space. In this way, we are able to prove well-posedness of the resulting extended primal and dual-mixed continuous formulations, as well as of the associated Galerkin schemes. A priori error estimates and corresponding rates of convergence are also established for both discrete methods. Finally, we provide numerical examples confronting our formulations with the standard ones, which prove our finite element methods to be particularly more efficient on the registration of translations and rotations, in addition for the dual-mixed approach to be much more suitable for the quasi-incompressible case, and all the above without losing the flexibility to solve problems arising from more realistic scenarios such as the image registration of the human brain.
- ItemNumerical Analysis & No Regrets. Special Issue Dedicated to the Memory of Francisco Javier Sayas (1968-2019)(WALTER DE GRUYTER GMBH, 2022) Gatica, Gabriel N.; Heuer, Norbert; Meddahi, SalimThis is the preface of a special issue dedicated to the memory of Francisco Javier Sayas who passed away on April 2, 2019. The articles reflect Sayas' main research interests in the numerical analysis of partial differential equations, containing contributions on the scattering and propagation of acoustic and electromagnetic waves, and the analysis of discontinuous Galerkin schemes, boundary element methods, and coupled schemes. We discuss the main contributions of Sayas and give an overview of the results covered by this special issue.
- ItemOn the numerical analysis of nonlinear twofold saddle point problems(2003) Gatica, Gabriel N.; Heuer, Norbert; Meddahi, Salim
- ItemPhase-shifted Pulse Width Modulation with alternate zeros voltage for parallel connection of H-Bridges for High-Current Low-Voltage applications(IEEE, 2019) Verdugo, D.; Rojas, F.; Lillo, J.; Diaz, M.; Pereda Torres, Javier Eduardo; Gatica, Gabriel N.Phase-Shifted Modulation (PSM) applied to multilevel converters is an effective method for reducing the output THD. In this paper, a new unipolar PSM method is proposed to control internal circulating current of a high-current low-voltage power converter, composed of parallel connected H- Bridges. The proposed method reduces the H-bridge currents distortions and the power losses of the overall converter. Simulation results comparing the standard unipolar modulation with the proposed unipolar modulation technique are performed to demonstrate its effectiveness.
- ItemPrimal and Mixed Finite Element Methods for Deformable Image Registration Problems(2018) Barnafi, Nicolas; Gatica, Gabriel N.; Hurtado Sepúlveda, Daniel