Man

Thomas Führer

Profesor Asistente

Pontificia Universidad Católica de Chile

Santiago, Chile

Líneas de Investigación


Numerical Treatment of PDEs, Finite Element Method, Boundary Element Method, FEM-BEM-coupling Methods Numerical methods for variational inequalities Preconditioning of adaptive BEM, FEM Discontinuous Petrov-Galerkin methods Least-squares methods

Educación

  •  Technical Mathematics, TECHNISCHE UNIVERSITAT WIEN (VIENA). Austria, 2014
  •  Technical Physics, TECHNISCHE UNIVERSITAT WIEN (VIENA). Austria, 2011
  •  Technical Mathematics, TECHNISCHE UNIVERSITAT WIEN (VIENA). Austria, 2010

Experiencia Académica

  •   Postdoctoral Researcher and Project Assistant Full Time

    TECHNISCHE UNIVERSITAT WIEN (VIENA)

    Wien, Austria

    2017 - 2017

  •   Profesor Asistente Full Time

    PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE

    Facultad de Matemáticas

    Santiago, Chile

    2017 - At present

Formación de Capital Humano


-) Supervision of Master thesis:
o) Adaptive BEM und FEM-BEM-Kopplung für die Lamé-Gleichung (Gregor Mitscha-Eibl), Master's thesis, Vienna University of Technology, 2014. (Supervised by Dirk Praetorius and Thomas Führer)
o) DPG methods for Stokes problem (José Carvajal), Master's thesis, PUC, since 03/2020
-) Supervision of PhD thesis:
o) DPG methods for the quad-curl problem (Pablo Herrera), PhD thesis, PUC, since 01/2020 (together with Norbert Heuer)


Difusión y Transferencia


Charlas en congresos cientificos y charlas invitadas:
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2019
[46] DPG for plate bending, part II, 6th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2019. (21.01--25.01, Concepción, Chile)
[45] Problema de obstáculo y aproximaciones, Seminario Caleta Numérica, 2019. (11.10, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile)
[44] Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two, Reliable Methods of Mathematical Modeling (RMMM) 2019, 2019. (09.09-13.09, TU Wien, Vienna, Austria)
[43] A least-squares finite element method for the obstacle problem, The mathematics of finite elements and applications (MAFELAP) 2019, 2019. (18.06-21.06, Brunel University, London, Great Britain)
[42] Introduction to the DPG method: Abstract framework and applications, Partial Differential Equations Seminar, 2019. (26.06, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal)
[41] Ultraweak formulation of linear elliptic PDEs in nondivergence form and DPG approximation, Minimum Residual & Least-Squares Finite Element Methods 2019, 2019. (16.09-18.09, Humboldt-Universität zu Berlin, Berlin, Germany)
[40] Problemas Bi-Laplacianos -- Formulaciones variacionales, trazas y aproximaciones, Coloquio de Mátematica, Facultad de Matemáticas, 2019. (12.04, Pontificia Universidad Católica de Chile, Santiago, Chile)
2018
[39] On the DPG method for Signorini problems, 13th World Congress in Computational Mechanics, 2018. (22.07--27.07, New York, USA)
[38] Superconvergence in a DPG method for an ultra-weak formulation, Symposium Numerical PDE, 2018. (25.01, Pontificia Universidad Católica de Chile, Santiago, Chile)
[37] Problema de obstáculo y aproximaciones, Seminario de divulgación, IMC, 2018. (18.04, Pontificia Universidad Católica de Chile, Santiago, Chile)
[36] A Least-Squares method for the Obstacle Problem, XXXI Jornada de Matemática de la Zona Sur, 2018. (25.04-27.04, Universidad Austral de Chile, Valdivia, Chile)
[35] On the coupling of DPG and BEM, Symposium of the International Association for Boundary Element Methods (IABEM), 2018. (26.06--28.06, Paris, France)
[34] Superconvergent DPG methods for second order elliptic problems, Computational Methods in Applied Mathematics: CMAM-8, 2018. (03.07--05.07, Raubichi Sports Complex, Belarus)
[33] Stable multilevel splittings in __MATH0__, The Second Chilean Symposium on Boundary Element Methods (invited talk), 2018. (14.12, Valparaíso, Chile)
2017
[32] A linear Uzawa-type solver for nonlinear transmission problems, Encuentro anual de SOMACHI, 2017. (02.11-04.11, Universidad de Talca, Talca, Chile)
[31] On the DPG method for Signorini problems, Santiago Numérico III, 2017. (28.06-30.06, PUC, Santiago, Chile)
[30] Superconvergence in the DPG method with ultra-weak formulation, Minimum Residual & Least-Squares Finite Element Methods, 2017. (02.10-04.10, Portland State University, Portland, USA)
[29] A linear Uzawa-type solver for nonlinear transmission problems, BEM on the Saar 2017, 2017. (29.05-31.05, University of Saarbrücken, Saarbrücken, Germany)
[28] On the DPG method for Signorini problems, Austrian Numerical Analysis Day, 2017. (04.05-05.05, Paris Lodron University of Salzburg, Salzburg, Austria)
2016
[27] On the coupling of DPG and BEM, 5th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2016. (11.01-15.01, Concepción, Chile)
[26] El método DPG: Introducción y Extensiones, Seminario Ingeniería PUC (invited talk), 2016. (31.08, PUC, Santiago, Chile)
[25] Robust coupling of DPG and BEM for a singularly perturbed transmission problem, The mathematics of finite elements and applications (MAFELAP) 2016, 2016. (14.06-17.06, Brunel University, London, Great Britain)
[24] Sobre el acomplamiento de DPG con BEM, XXIX Jornada de Matemática de la Zona Sur, 2016. (21.04-23.04, Universidad de Talca, Santa Cruz, Chile)
[23] Robust coupling of DPG and BEM for a singularly perturbed transmission problem, International Conference on Boundary and Interior Layers (BAIL) 2016, 2016. (14.08-19.08, CSRC, Beijing, China)
[22] On the coupling of DPG and BEM, The First Chilean Symposium on Boundary Element Methods (invited talk), 2016. (14.12, PUC, Santiago, Chile)
2015
[21] A wirebasket preconditioner for the mortar boundary element method, Caleta Numérica (invited talk), 2015. (12.06, PUCV, Valparaíso, Chile)
[20] Multilevel methods for the hypersingular integral equation on locally refined triangulations, La Serena Numérica II, 2015. (14.01-16.01, La Serena, Chile)
[19] A wirebasket preconditioner for the mortar boundary element method, Seminar (invited talk), 2015. (09.06, Universidad del Bío Bío, Concepción, Chile)
[18] Optimal preconditioning for the coupling of adaptive FEM and BEM, 1st Pan-American Congress on Computational Mechanics (PANACM 2015), 2015. (27.04-29.04, Buenos Aires, Argentina)
[17] DPG method with optimal test functions for a fractional advection diffusion equation, XXIV Congreso de Matemática CAPRICORNIO (COMCA 2015), 2015. (05.08-07.08, Iquique, Chile)
2014
[16] Optimal preconditioning for the coupling of adaptive FEM and BEM, 12th Workshop on Fast Boundary Element Methods in Industrial Applications, 2014. (25.09-28.09, Hirschegg/Kleinwalsertal, Austria)
[15] Optimal preconditioning for the coupling of adaptive FEM and BEM, Seminar (invited talk), 2014. (11.09, Leibniz Universität Hannover, Hannover, Germany)
[14] Coupling of FEM and BEM: adaptivity and preconditioning, Seminar (invited talk), 2014. (20.11, TU Graz, Graz, Austria)
[13] Optimal preconditioning for the coupling of adaptive finite elements and boundary elements, 11th World Congress on Computational Mechanics (WCCM XI), 2014. (20.07-25.07, Barcelona, Spain)
[12] Efficient additive Schwarz preconditioning of the hypersingular integral equation on locally refined triangulations, Doctoral Program on Dissipation and Dispersion nPDEs (Seminar), 2014. (22.01, Vienna University of Technology, Austria)
2013
[11] Convergence of adaptive FEM-BEM coupling, 4th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2013. (14.01-18.01, Concepción, Chile)
[10] Efficient additive Schwarz preconditioning of the hypersingular integral equation on locally refined triangulations, 11th Workshop on Fast Boundary Element Methods in Industrial Applications, 2013. (26.09-29.09, Hirschegg/Kleinwalsertal, Austria)
[9] FEM-BEM couplings without stabilization, Symposium of the International Association for Boundary Element Methods (IABEM), 2013. (09.01-11.01, Santiago de Chile, Chile)
[8] Additive Schwarz methods for non-symmetric FEM-BEM couplings on locally refined meshes, Seminar (invited talk), 2013. (05.07, Leibniz Universität Hannover, Hannover, Germany)
[7] Stability of FEM-BEM couplings for nonlinear elasticity problems, 9th Austrian Numerical Analysis Day, 2013. (11.04-12.04, Graz, Austria)
2012
[6] FEM-BEM coupling without stabilization, 10th Workshop on Fast Boundary Element Methods in Industrial Applications, 2012. (27.09-30.09, Hirschegg/Kleinwalsertal, Austria)
[5] Convergence of adaptive FEM-BEM coupling driven by residual-based error estimators, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 2012. (10.09-14.09, Vienna, Austria)
[4] Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity, BEM on the Saar 2012, 2012. (12.05-16.05, Universität des Saarlandes, Saarbrücken, Germany)
[3] Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity, 8th Austrian Numerical Analysis Day, 2012. (10.05-11.05, Vienna University of Technology, Austria)
2010
[2] Computing the magnetostatic potential, Numerik-Statusseminar Ulm und Wien, 2010. (25.08-29.08, Kleinarl, Austria)
2009
[1] Computing the magnetostatic potential, Numerik-Statusseminar Ulm und Wien, 2009. (12.09-19.09, Cortona, Italy)



 

Article (45)

MULTILEVEL DECOMPOSITIONS AND NORMS FOR NEGATIVE ORDER SOBOLEV SPACES
A Locking-Free DPG Scheme for Timoshenko Beams
A robust DPG method for large domains nbsp;
Analysis of Backward Euler Primal DPG Methods
Space-time least-squares finite elements for parabolic equations
The double adaptivity paradigm: (How to circumvent the discrete inf–sup conditions of Babuška and Brezzi)
Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation
A short note on plain convergence of adaptive least-squares finite element methods
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
First-order least-squares method for the obstacle problem
Trace operators of the bi-Laplacian and applications
Adaptive BEM with inexact PCG solver yields almost optimal computational costs
Adaptive Uzawa algorithm for the Stokes equation
AN ULTRAWEAK FORMULATION OF THE KIRCHHOFF-LOVE PLATE BENDING MODEL AND DPG APPROXIMATION
Fully discrete DPG methods for the Kirchhoff-Love plate bending model
New a priori analysis of first-order system least-squares finite element methods for parabolic problems
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems
A wirebasket preconditioner for the mortar boundary element method
Combining the DPG Method with Finite Elements
On the DPG method for Signorini problems
Optimal Quasi-diagonal Preconditioners for Pseudodifferential Operators of Order Minus Two
Superconvergence in a DPG method for an ultra-weak formulation
A time-stepping DPG scheme for the heat equation
DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation
LOCAL INVERSE ESTIMATES FOR NON-LOCAL BOUNDARY INTEGRAL OPERATORS
On the coupling of DPG and BEM
Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations
Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements
Robust coupling of DPG and BEM for a singularly perturbed transmission problem
Adaptive boundary element methods for optimal convergence of point errors
Efficient numerical computation of direct exchange areas in thermal radiation analysis
Adaptive boundary element methods=> A posteriori error estimators, adaptivity, convergence, and implementation
Energy norm based error estimators for adaptive BEM for hypersingular integral equations
Optimal additive Schwarz methods for the hp-BEM=> the hypersingular integral operator in 3D on locally refined meshes
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation - Part II=> Hyper-singular integral equation
Stability of symmetric and nonsymmetric FEM–BEM couplings for nonlinear elasticity problems
Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems
HILBERT — a MATLAB implementation of adaptive 2D-BEM
Multiscale modeling in micromagnetics=> Existence of solutions and numerical integration
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I=> weakly-singular integral equation
ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve
Classical FEM-BEM coupling methods=> nonlinearities, well-posedness, and adaptivity
Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations
Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods

ConferencePaper (1)

Superconvergent DPG Methods for Second-Order Elliptic Problems

Proyecto (3)

Minimum residual methods for linear flow problems
Least-squares methods for obstacle problems
PRECONDITIONED LINEAR SOLVERS FOR NONCONFORMING BOUNDARY ELEMENTS
28
Thomas Führer

Profesor Asistente

Facultad de Matemáticas

Pontificia Universidad Católica de Chile

Santiago, Chile

6
Norbert Heuer

Profesor Titular

Matemática

Pontificia Universidad Católica de Chile

Santiago, Chile

4
Michael Karkulik

Profesor Asistente

Departamento de Matemática

UNIVERSIDAD TECNICA FEDERICO SANTA MARIA

Valparaíso, Chile

1
Rodolfo Rodriguez

Full Professor

Ingeniería Matemática

UNIVERSIDAD DE CONCEPCION

Concepción, Chile