C. Jerez-Hanckes' Research

Carlos Jerez-Hanckes

Associate Professor in Numerical Analysis

KTH Royal Institute of Technology, Stockholm

Wave propagation · Boundary integral equations · Computational electromagnetics · Uncertainty quantification

Everything in the cosmos is propagated in the means of waves

- Leonardo da Vinci, Codex Atlanticus

I develop mathematical and computational methods for wave propagation, with a particular focus on boundary integral equations, computational electromagnetics, and uncertainty quantification.

My research combines numerical analysis, operator theory, and scientific computing to develop accurate and efficient methods for scattering and transmission problems in complex and uncertain geometries. Current interests include multiple trace formulations, operator preconditioning, high-order methods for screens and gratings, and the parametric dependence of wave problems on geometry.

These methods are motivated by applications ranging from electromagnetic scattering and photonics to bioelectricity and wave propagation in complex media.

Main Areas of Research

Boundary Integral Equations & Wave Scattering

Multiple trace formulations, Calderón/operator preconditioning, transmission problems and fast boundary element solvers.

Computational Electromagnetics

Numerical methods for Maxwell problems, including boundary and volume formulations, geometric approximation and high-frequency scattering.

Uncertainty & Parametric Dependence

Shape uncertainty, domain-to-solution maps, parametric regularity and holomorphic dependence of wave scattering operators.

High-Order Methods for Complex Geometries

Spectral Galerkin and high-order discretizations for screens, open arcs, gratings and other geometrically challenging scattering configurations.

At ALMA Observatory, Atacama Desert, Chile (2020)

At the Oberwolfach Mathematisches Forschungsinstitut, Germany (2020)

About me (professionally)

I am currently spending a sabbatical year at the University of Bath as the recipient of the David Parkin Visiting Professorship, working within the Department of Mathematical Sciences alongside Prof. Euan Spence.

Since 2019, I have been Full Professor at Universidad Adolfo Ibáñez (UAI), Santiago, Chile, until 2025. I also served as Dean of the the Faculty of Engineering and Sciences at UAI. During this period, I was appointed Executive Director of the Data Observatory Foundation, directly reporting to Chilean Ministers of Economy and Science and Technology.

Between 2011 and 2018 I was first Assistant and then Associate Professor at the School of Engineering at Pontificia Universidad Católica de Chile (PUC), Santiago, Chile, where I also became the founding Director of the Institute for Mathematical and Computational Engineering (IMCE)—an interdisciplinary center focused on applied mathematics and computing.

My international academic path includes:

Visiting Professorship at the Seminar for Applied Mathematics (SAM), ETH Zurich (2018–2019);
A Luksic scholarship to collaborate with Profs. P. Fay and R. McClarren at the University of Notre Dame (2017);
An Erasmus Mundus Visiting Scholar appointment at TU Delft and KTH Stockholm for their Computer Simulations for Science and Engineering (COSSE) join Master’s Program (2016),
And a Postdoctoral Fellowship at SAM under Prof. Ralf Hiptmair (2009–2011).

I obtained my Ph.D. in Applied Mathematics in 208 at École Polytechnique, France, at its Centre de Mathématiques Appliquées (CMAP), under the supervision of Prof. Jean-Claude Nédélec and Prof. Vincent Laude, with support from a CIFRE scholarship co-funded by EPCOS A.G (now TDK). I hold B.Eng.Sc. (2002) and M.Eng.Sc. (2005) degrees in Electrical and Industrial Engineering from PUC, Chile.

From 2018 until 2024, I served on the Frank Rizzo Award Committee of the International Association for Boundary Element Methods (IABEM) and am now elected member of its Executive Committee. I am also member of the AMS, SIAM and IEEE AP and UFFC communities.

Recent Seminar Invited Talks

2025 May 15, UNIVERSITY OF CAMBRIDGE, UK, Applied and Computational Analysis Series, DAMTP. Talk: New Insights on High Wave Scattering by Multiple Open Arcs: Exponentially Convergent Methods and Shape Holomorphy
2025 Feb 25, UNIVERSITY OF BIRMINGHAM, UK, Optimisation & Numerical Analysis Seminar, School of Mathematics. Talk: An Invitation to Domain Uncertainty Quantification in Computational Electromagnetics
2024 Dec 10, UNIVERSITY OF BATH, UK, Applied and Interdisciplinary Mathematics Seminar, Department of Mathematical Sciences. Talk: Cell Electropermeabilization Modeling Via Multiple Traces Formulation and Time Semi-Implicit Multistep Coupling
2024 Nov 20, ETH ZURICH, SWITZERLAND, Zurich Colloquium on Applied Mathematics, Talk: New Insights on Wave Scattering by Multiple Open Arcs: Lightning-Fast Methods and Shape Holomorphy
2024 Nov 14, ENSTA PARISTECH PARIS, FRANCE, Numerical Analysis Seminar, Laboratoire POems, Talk: Bi-parametric (Fast) Operator Preconditioning and Applications to Wave Scattering Problems
2024 Nov 5, EPFL LAUSANNE, SWITZERLAND, Numerical Analysis Seminar, Talk: An Invitation to Shape Uncertainty Quantification in Computational Electromagnetics
2024 Oct 21, CHALMERS GOTHENBURG, SWEDEN, Numerical Analysis Seminar, Talk: Cell Electropermeabilization Modeling Via Multiple Traces Formulation and Time Semi-Implicit Multistep Coupling
2024 Oct 18, UNIVERSITY OF MANCHESTER, UK, Numerical Analysis Seminar, Talk: An Invitation to Domain Uncertainty Quantification in Computational Electromagnetics
2024 Oct 9, UCL/IMPERIAL COLLEGE LONDON, UK, Numerical Analysis Seminar, Department of Mathematics, Talk: New Insights on Wave Scattering by Multiple Open Arcs: Lightning-Fast Methods and Shape Holomorphy
2024 May 3, UNIVERSITY OF BATH, UK, Numerical Analysis Seminar, Department of Mathematical Sciences, Talk: Multiple Traces Formulation: a marriage between Boundary Integral and Domain Decomposition Methods
2021 Oct 14, CHINESE ACADEMY OF SCIENCES, BEIJING, CHINA, Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Talk: High order Galerkin methods for Helmholtz scattering in quasi-periodic layered media and screens
2018 Dec 5, TECHNISCHE UNIVERSITÄT GRAZ, AUSTRIA, Institut für Numerische Mathematik, Talk: Time-domain electric excitation of biological cells modeling using BIEs
2018 Oct 24, UNIVERSITA DEGLI STUDI DI PAVIA, ITALY, Dipartimento di Matematica “F. Casorati”, Talk: High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs
2017 Jun 11–17, NORGES ARKTISKE UNIVERSITET, NARVIK, NORWAY, Institutt for datateknologi og beregningsorienterte ingeniørfag, Talk: Wave diffraction by random surfaces: Uncertainty Quantification by Sparse Tensor Approximation
2016 Nov 29–Dec 12, UNIVERSITÉ PIERRE ET MARIE CURIE, PARIS, FRANCE, Laboratoire Jacques-Louis Lions, Talk: Electromagnetic wave scattering by random surfaces: Uncertainty Quantification via Sparse Tensor BEM
2016 Aug 28–Sep 6, TEXAS A&M UNIVERSITY, COLLEGE STATION, USA, Department of Nuclear Engineering, Talk: Wave Diffraction by Random Shape Scatterers: Uncertainty Quantification by Sparse Tensor Approximation
2015 May 13, UNIVERSIDAD DE CONCEPCIÓN, CHILE, Coloquio del Departamento de Ingeniería Matemática, Talk: Multiple traces formulation for high-frequency scattering
2012 Sep 27, CI2MA-DMAT UBB, CONCEPCIÓN, CHILE, Seminario de Análisis Numérico y Modelación Matemática, Talk: Sparse Tensor Edge Elements
2012 Aug 24, PONTIFICIA UNIVERSIDAD CATÓLICA DE VALPARAÍSO, CHILE, Seminar on Numerical Analysis and Applied Mathematics, Talk: Sparse Tensor Galerkin Approximations for Moment Analysis
2010 Sep 29, ETH ZURICH, SWITZERLAND, Seminar für Angewandte Mathematik, Talk: Variational forms for the inverses of integral logarithmic operators over an interval
2010 Jun 15–17, TECHNISCHE UNIVERSITÄT GRAZ, AUSTRIA, Institut für Numerische Mathematik, Talk: Multiple traces formulation for Helmholtz transmission problems
2010 Jan 25-28, INSTITUT ÉLIE CARTAN DE NANCY, FRANCE, Séminaire d’Équations aux Dérivées Partielles et Applications, Talk: Spectral Galerkin Boundary Element Method for Interface Problems
2009 Mar 10, ETH ZURICH, Colloquium on Electromagnetics and THz Electronics, Talk: On the application of Finite Elements/Boundary Element methods
2008 Jun 25, UNIVERSITE ́ D’ORSAY, FRANCE, Laboratoire de Mathématiques, Talk: A hybrid boundary bases Galerkin method for modelling flat structures in 3-D
2008 Jun18, UNIVERSITY OF OSLO, Centre of Mathematics for Applications. Talk: 3-D Wave Propagation in Piezoelectric Devices: A hybrid Galerkin bases approach

Conferences and Workshops (Invited Talks)

TBD, MS Numerical and computational methods for wave equations, Advanced COmputational Methods in ENgineering and Applied Mathematics (ACOMEN) 2025, Ghent, Belgium, Sep 15–19, 2025
TBD, International Conference on Monte Carlo Methods and Applications (MCM) 2025, Illinois Institute of Technology, Chicago, US, Jul 28–Aug 1, 2025
Bi-parametric operator preconditioning: Theory and applications, Bath/Rutherford Appleton Laboratory (RAL) Day 2025, Didcot, UK, Apr 10, 2025
Finite Element Approximations for Maxwell Variational Problems on Curved Domains: Domain and Quadrature Effects, Advanced Solvers for Frequency-Domain Wave Problems and Applications, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, Jan 20–24, 2025
Shape Uncertainty Quantification for Electromagnetic Waves Scattering via First-Order Sparse Boundary Element Approximation, MS Computational Electromagnetism, Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2024), Concepción, Chile, Jan 15–19, 2024.
Spectral Galerkin Method For Solving Elastic Wave Scattering Problems With Multiple Open Arcs, MS Recent Advances in BEM for Complex Domains, Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2024), Concepción, Chile, Jan 15–19, 2024.
Multilevel Domain Uncertainty Quantification In Computational Electromagnetics, MS Novel Multilevel Methods for Uncertainty Quantification, SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam, Netherlands, Feb 26–Mar 3, 2023.
Uncertainty Quantification for Multigroup Diffusion Equations Using Sparse Tensor Approximations, MS: Multilevel and Multiresolution Methods in Uncertainty Quantification, International Multigrid Conference, Lugano, Switzerland, Aug 22–26, 2022.
Helmholtz Scattering By Random Domains: First-Order Sparse Boundary Element Approximation, Computational Uncertainty Quantification: Mathematical Foundations, Methodology, and Data, Erwin Schrödinger Institute, Vienna, Austria, June 5–17, 2022.
Domain Uncertainty Quantification in Computational Electromagnetics, Shape Uncertainty Quantification and Applications at SIAM UQ 2020, TU Muenchen, Munich, Germany, Mar 24–27, 2020 (cancelled).
Spectral Non-Conforming BEM for local Multiple Trace Formulations, Workshop on Boundary Element Methods, Mathematisches Forschungsinstitut Oberwolfach, Germany, Feb 2–8, 2020.
Fast Calderón Preconditioning for Helmholtz Boundary Integral Equations, 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), Vienna, Austria, Aug 25–30, 2019.
–, MAFELAP 2019, Brunel University, Uxbridge, England, June 18–21, 2019.
High-order Galerkin Method for Helmholtz and Laplace Problems on Multiple Open Arcs, 14th Annual Conference on Frontiers in Applied and Computational Mathematics (FACM 2018), New Jersey, USA, Aug 24–26, 2018.
Electromagnetic wave scattering by random surfaces: shape holomorphy and sparse tensor approximations, ND-PUC Minisymposium on Uncertainty Quantification, South Bend, USA, Aug 20, 2018.
Multiscale analysis of myelinated axons, Disentis NumPDE Summer Retreat 2018, Disentis, Switzerland, Aug 8–10, 2018.
–, Symposium Numerical PDE, Pontificia Universidad Cato ́lica de Chile, Santiago, Chile, Jan 25, 2018.
Electromagnetic Wave Scattering By Random Surfaces: Uncertainty Quantification Via Sparse Tensor Boundary Elements, The First Chilean Symposium on Boundary Element Methods: Efficient computational algorithms for simulating wave propagation, Santiago, Chile, Dec 14, 2016.
Multiple Traces Formulations: Novel Extensions and Challenges, Minisymposium: Numerical Methods for the Variable-Medium High-Frequency Helmholtz Equation, 2016 SIAM Annual Meeting, Boston, USA, Jul 11–15, 2016.
Multiple Traces Formulation: Preconditioning Strategies, Minisymposium: Waves, 13th Annual Conference on Frontiers in Applied and Computational Mathematics (FACM 2016), New Jersey, USA, Jun 3–4, 2016.
Optimal Preconditioning for the Hypersingular Operators on Screens, Fifty Years of Hearing Drums: Spectral Geometry and the Legacy of Mark Kac, Santiago, Chile, May 16–20, 2016.
13. Electromagnetic wave scattering by random surfaces: Shape holomorphy, Minisymposium: Computational Electromagnetism, Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Universidad de Concepción (WONAPDE 2016), Concepción, Chile, Jan 11–15, 2016.
12. Multiple traces formulation for multiple biological cells electrically excited, Minisymposium: Computational Cardiac Biomechanics, Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Universidad de Concepción (WONAPDE 2016), Concepción, Chile, Jan 11–15, 2016.
Wave scattering by randomly perturbed periodic gratings via sparse tensor BEM, Minisymposium: Advances in Finite and Boundary Elements, Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Universidad de Concepción (WONAPDE 2016), Concepción, Chile, Jan 11–15, 2016.
Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements, 2nd Chongqing Workshop on Computational and Applied Mathematics, Chongqing, China, Aug 16–19, 2015.
Local Multiple Traces Formulation for High-Frequency Scattering, The 12th International Conference on Mathematical and Numerical Aspects of Wave Propagation - Waves 2015, Karlsruhe, Alemania, Jul 20–24, 2015.
Sparse Tensor Approximation for Uncertainty Quantification on 2D Periodic Gratings, 36th Progress in Electromagnetics Research 2015 - PIERS 2015, Prague, Czech Republic, Jul 5–8, 2015.
Formulacio ́n en integrales de borde y acoplamiento no lineal en el tiempo para la modelación de axones bajo estimulación eléctrica (Engl. transl. Boundary Integral Formulations and coupling to non-linear time domain equation for modeling axons under electric stimulation, Jornada de Modelacio ́n en Biomedicina(Engl. transl. Workshop in Biomedical Modelling), Universidad de Chile, Jun 4, 2015.
Operator Preconditioning of Screen Integral Formulation, Tercer Encuentro en Aplicaciones de la Matemática, Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Dec 2012.
Multiple Traces Formulation for Helmholtz Transmission Problems, Segundo Encuentro en Aplicaciones de la Matematica, Instituto de Matema ́ticas, Pontificia Universidad Cato ́lica de Valpara ́ıso, Jan 2012.
—, CI2MA Second Focus Seminar “Computational Electromagnetism”, Universidad de Concepción, Jan 2012. 3. Operational preconditioning for 2-D screen and fracture problems using BEM, Sexto Encuentro de Análisis
Nume ́rico de Ecuaciones Diferenciales Parciales (La Serena Numérica I), La Serena, Chile, Dec 2011.
Multiple Traces Boundary Integral Formulation for Helmholtz Transmission Problems, 2010 ISFMA Symposium, Maxwell’s Equations: Theoretical and Numerical Issues with Applications, Shanghai, China, Jul 2010.
Hybrid Galerkin method for elliptic and wave propagation problems in R3 over planar structures, The Tenth International Conference on Integral Methods in Science and Engineering, IMSE 2008 Santander, Spain, Jul 2008.

Conferences and Workshops (Contributed Talks)

Local Multiple Traces Formulation for Elastic Wave Scattering by Heterogeneous Scatterers, Symposium of the International Association for Boundary Element Methods, IABEM 2024, Hong Kong SAR, China
Shape Uncertainty Quantification for Electromagnetic Wave Scattering via First-Order Sparse Boundary Element Approximation, 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, WAVES 2024, Berlin, Germany, Jul 1–5, 2024.
Finite-Element Domain Approximation For Maxwell Variational Problems on Curved Domains, Numerical Analysis Workshop, British Mathematical Colloquium 2024, Manchester, UK, June 17–20, 2024.
Bi-parametric Operator Preconditioning, International Conference on Preconditioning Techniques for Scientific and Industrial Applications, Precond 2024, Atlanta, USA, June 10–12, 2024.
Exponentially Convergent Spectral Galerkin BEM for Elastic Wave Scattering of Cracks, 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2022), July 24–29, 2022.
High-order Galerkin Method for Helmholtz and Laplace Problems on Multiple Open Arcs, 16th Workshop Fast Boundary Element Methods in Industrial Applications, Söllerhaus, Austria, Oct 4–7, 2018.
Spectral Galerkin Method for Solving Helmholtz and Laplace Dirichlet Problems on Multiple Open Arcs, ICOSAHOM 2018, London, England, Jul 9–13, 2018.
Multiple Traces Formulation and Semi-Implicit Scheme for Modelling Biological Cells under Electrical Stimulation, IABEM 2018, Paris, France, Jun 26–28, 2018.
Boundary Integral Formulation for Helmholtz and Laplace Dirichlet Problems On Multiple Open Arcs, IABEM 2018, Paris, France, Jun 26–28, 2018.
Spectral Galerkin Method for Solving Helmholtz and Laplace Dirichlet Problems on Multiple Open Arcs, ECCM-ECFD 2018, Glasgow, Scotland, Jun 11–15, 2018.
Multiscale analysis of myelinated axons, 8th International Conference on Multiscale Modeling 2018, Santiago, Chile, Jan 7, 2018.
Wave Diffraction by Random Surfaces: Non-Conforming Sparse Tensor Boundary Elements, Frontiers of Uncertainty Quantification in Engineering (FrontUQ), Technical University Muenchen, Germany, Sep 5-8, 2017.
Fast Caldero ́n Preconditioning for the Electric Field Integral Equation, Innovations in Wave Modelling 2017, Nottingham, UK, Jul 12–14, 2017.
Multiple traces formulation and semi-implicit scheme for modeling packed cells under electrical stimulation, Santiago Numérico III, Noveno Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, Santiago, Chile, Jun 28–30, 2017.
Wave Diffraction by Random Surfaces: Uncertainty Quantification via Sparse Tensor Boundary Elements, WAVES 2017: 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2017, Minneapolis, USA, May 15–19, 2017.
Boundary Integral Formulation And Semi-Implicit Scheme For Modeling Packed Cells Under Electrical Stimulation, Seventh International Conference on Multiscale Modelling and Methods: Upscaling in Engineering and Medicine, Santiago, Chile, Jan 16–17, 2017.
Uncertainty Quantification for Electromagnetic Scattering by 1D PEC Gratings, Seventh Valparaiso’s Mathematics and Applications Days (VMAD-7), Valpara ́ıso, Chile, Jan 12–13, 2017.
Sparse Tensor Approximation for Uncertainty Quantification on 2D Periodic Gratings, 36th Progress in Electromagnetics Research 2015 - PIERS 2015, Prague, Czech Republic, Jul 5–8, 2015.
Multiple Traces Formulation for High-Frequency Scattering, I Pan-American Congress on Computational Mechanics - PANACM 2015, Buenos Aires, Argentina, Apr 27–29, 2015.
Boundary Integral Formulation for the Electrical Response of Biological Cells to External Electrical Stimulations, Octavo Encuentro de Ana ́lisis Nume ́rico de Ecuaciones Diferenciales Parciales (La Serena Numérica II), La Serena, Chile, Jan 2015.
First-Order Second Moment Sparse Tensor Approximation of Maxwell Scattering by Randomly Shaped Objects, Latest Advances in Numerical Solutions with FEM, Puerto Varas, Chile, Sep 2014.
Local Multiple Traces Formulation for Scattering Problems: Extension to Spectral Elements, 6th International Conference on Advanced Computational Methods in Engineering, ACOMEN 2014, Ghent, Belgium, Jun 2014.
Local multiple traces formulation for high frequency scattering, DD22 International Conference on Domain Decomposition Methods, Lugano, Sep 2013.
Existence and uniqueness of Maxwell harmonic waves for an impedance half-space, Journées Singulières Augmentées 2013, Rennes, France, Aug 2013.
Operator Preconditioning for Two-Dimensional Screen and Fracture Problems Using Boundary Elements, Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations - WONAPDE 2013, Concepción, Chile, Jan 7–11, 2013.
Multiple traces boundary integral formulation for scattering problems, 10th World Congress On Computational Mechanics, Sao Paulo, Jul 2012.
Electrostatic Modeling of a Needle-Catheter System used in Peripheral Nerve Stimulation, 6th International Conference on Bioinformatics and Biomedical Engineering, ICBBE 2012, Shanghai, China, May 17-20, 2012.
Multiple Traces Formulation for Helmholtz Transmission Problems, LXXX Encuentro Anual Sociedad Matema ́tica de Chile, Nov 2011.
—, Jornada de Meca ́nica Computacional, Pontificia Universidad Católica de Chile, Santiago, Chile, Oct 2011.
Multiple Traces Boundary Integral Formulation for Helmholtz Transmission Problems, 8th Workshop Fast Boundary Element Methods in Industrial Applications, Austria, Sep–Oct 2010.
—, The Eleventh International Conference on Integral Methods in Science and Engineering, IMSE 2010, Brighton, UK, Jul 2010.
—, 6th Workshop on Advanced Computational Electromagnetics (ACE 10), Zurich, Switzerland, Jul 2010.
—, Quinto Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, Santiago Numérico II, Santiago, Chile, Jan 2010.
Spectral Galerkin Boundary Element Method for Interface Problems, Third Chilean Workshop on Numerical Analysis of Partial Differential Equations - WONAPDE 2010, Concepción, Chile, Jan 2010.
Hybrid boundary elements scheme for modeling flat structures in R3, Cuarto Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, Santiago Numérico I, Santiago, Chile, Jan 2009.
A hybrid BEM formulation for Surface Acoustic Wave Interdigital transducers modelling, 6th Workshop Fast Boundary Element Methods in Industrial Applications, Austria, Oct 2–5, 2008.

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