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A High-Order Ultraweak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements
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Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation
Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation
Christoph Erath, Lorenzo Mascotto, Jens M. Melenk, Ilaria Perugia and Alexander Rieder Journal of Scientific Computing 92(1) (2022) https://doi.org/10.1007/s10915-022-01849-0
A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
Lise-Marie Imbert-Gérard, Andrea Moiola and Paul Stocker Mathematics of Computation 92(341) 1211 (2022) https://doi.org/10.1090/mcom/3786
Finite Element Method for a Nonlinear Perfectly Matched Layer Helmholtz Equation with High Wave Number
Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media
Tak Shing Au Yeung, Ka Chun Cheung, Eric T. Chung, Shubin Fu and Jianliang Qian Journal of Computational Physics 465 111380 (2022) https://doi.org/10.1016/j.jcp.2022.111380
An efficient neural network method with plane wave activation functions for solving Helmholtz equation
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 363 (2022) https://doi.org/10.1007/978-3-030-95319-5_9
Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems
A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation
A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations
Håkon Sem Fure, Sébastien Pernet, Margot Sirdey and Sébastien Tordeux SN Partial Differential Equations and Applications 1(4) (2020) https://doi.org/10.1007/s42985-020-00024-0
Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number
Bernstein–Bézier based finite elements for efficient solution of short wave problems
A. El Kacimi, O. Laghrouche, M.S. Mohamed and J. Trevelyan Computer Methods in Applied Mechanics and Engineering 343 166 (2019) https://doi.org/10.1016/j.cma.2018.07.040
Adaptive refinement for hp–Version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
A nonconforming Trefftz virtual element method for the Helmholtz problem
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler Mathematical Models and Methods in Applied Sciences 29(09) 1619 (2019) https://doi.org/10.1142/S0218202519500301
The method of polarized traces for the 3D Helmholtz equation
A nonconforming Trefftz virtual element method for the Helmholtz problem: Numerical aspects
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler Computer Methods in Applied Mechanics and Engineering 347 445 (2019) https://doi.org/10.1016/j.cma.2018.12.039
Numerical Mathematics and Advanced Applications ENUMATH 2017
Scott Congreve, Joscha Gedicke and Ilaria Perugia Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 493 (2019) https://doi.org/10.1007/978-3-319-96415-7_44
A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems
The size function for a HDG method applied to the Helmholtz problem
Anna Regina Corbo, Eduardo Gomes Dutra do Carmo, Webe João Mansur and Katia Prado Fernandes Computational and Applied Mathematics 38(3) (2019) https://doi.org/10.1007/s40314-019-0861-1
Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation
Scott Congreve, Joscha Gedicke and Ilaria Perugia SIAM Journal on Scientific Computing 41(2) A1121 (2019) https://doi.org/10.1137/18M1207909
A typical backward substitution method for the simulation of Helmholtz problems in arbitrary 2D domains
Performance analysis of the ultra weak variational formulation to compute electromagnetic fields on nonuniform meshes
Alfred Gimpel, Elson J. Silva and Marcio M. Afonso International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 31(2) (2018) https://doi.org/10.1002/jnm.2228
Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation
A priorierror analysis of space–time Trefftz discontinuous Galerkin methods for wave problems
Fritz Kretzschmar, Andrea Moiola, Ilaria Perugia and Sascha M. Schnepp IMA Journal of Numerical Analysis 36(4) 1599 (2016) https://doi.org/10.1093/imanum/drv064
High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Ralf Hiptmair, Andrea Moiola and Ilaria Perugia Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 237 (2016) https://doi.org/10.1007/978-3-319-41640-3_8
An Unconditionally Stable Discontinuous Galerkin Method for the Elastic Helmholtz Equations with Large Frequency
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Daniel Peterseim Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 343 (2016) https://doi.org/10.1007/978-3-319-41640-3_11
A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation
Numerical Mathematics and Advanced Applications - ENUMATH 2013
Paola F. Antonietti, Ilaria Perugia and Zaliani Davide Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 557 (2015) https://doi.org/10.1007/978-3-319-10705-9_55
Efficient DG‐like formulation equipped with curved boundary edges for solving elasto‐acoustic scattering problems
Hélène Barucq, Rabia Djellouli and Elodie Estecahandy International Journal for Numerical Methods in Engineering 98(10) 747 (2014) https://doi.org/10.1002/nme.4652
On Trefftz and weak Trefftz discontinuous Galerkin approaches for medium-frequency acoustics
Dispersion analysis of plane wave discontinuous Galerkin methods
Claude J. Gittelson and Ralf Hiptmair International Journal for Numerical Methods in Engineering 98(5) 313 (2014) https://doi.org/10.1002/nme.4626
Domain Decomposition Methods in Science and Engineering XXI
T. Betcke, M. J. Gander and J. Phillips Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXI 98 577 (2014) https://doi.org/10.1007/978-3-319-05789-7_55
A local wave tracking strategy for efficiently solving mid- and high-frequency Helmholtz problems
M. Amara, S. Chaudhry, J. Diaz, R. Djellouli and S.L. Fiedler Computer Methods in Applied Mechanics and Engineering 276 473 (2014) https://doi.org/10.1016/j.cma.2014.03.012
Implementation of an interior point source in the ultra weak variational formulation through source extraction