PhD research topic - Maria Lopez Fernandez

Maria Lopez Fernandez

Research areas

Numerical analysis of evolutionary problems, numerical complex analysis


Wave scattering problems, boundary integral equations, convolution equations, retarded potentials, fractional differential equations, contour integral methods, adaptivity, fast algorithms

Research topics

The efficient resolution of exterior wave problems, both acoustic and electromagnetic, have become an active field of research in the last decade. A well established approach to deal with the possibly unboundedness of the computational domain in the reformulation of the problems as time-domain boundary integral equations. In this way the computational domain becomes the bounded surface of the scatterers. The main difficulties arising in the space-time discretizazion of the resulting retarded integral equations are the numerical stability, the computational cost and the memory requirements. Several strategies have been proposed to overcome these bottlenecks and are currently under study: introduction of time-space adaptivity, hierarchical matrix techniques to deal with associated high-frequency problems, convolution quadrature methods, etc.

Other models involving time-convolution integral equations are Partial Differential Equations of fractional order and nonlinear Schrödinger equations with concentrated potentials. The design of efficient, memory-saving and adaptive algorithms for these problems is of topical interest.


[1] L. Banjai, M. L\'opez-Fern\'andez, A. Sch\"adle, Fast and oblivious convolution quadrature for dissipative and two-dimensional wave equations, SIAM Journal on Numerical Analysis 55 (2017), pp.~621--639.

[2] M. Lopez-Fernandez and S. Sauter, Generalized Convolution Quadrature with Variable Time Stepping, IMA J. Numer. Anal. 33 (2013), 1156-1175.

[3] F.-J. Sayas, Retarded Potentials and Time Domain Boundary Integral Equations. Springer Series in Computational Mathematics, 50, 2016.


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