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A High-Order Ultraweak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements
Timo Lähivaara, William F. Hall, Matti Malinen, Dale Ota, Vijaya Shankar and Peter Monk IEEE Transactions on Antennas and Propagation 72(5) 4440 (2024) https://doi.org/10.1109/TAP.2024.3373063
Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties
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
Finite Element Method for a Nonlinear Perfectly Matched Layer Helmholtz Equation with High Wave Number
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 Trefftz Discontinuous Galerkin Method for the Linear Schrödinger 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
A Trefftz method with reconstruction of the normal derivative applied to elliptic equations
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
High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation
A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation
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
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
Trefftz approximations in complex media: Accuracy and applications
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 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
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
The method of polarized traces for the 3D Helmholtz equation
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
Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation
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
The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method
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
Substructuring Preconditioners for the Systems Arising from Plane Wave Discretization of Helmholtz Equations
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
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
Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime
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
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
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
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
Implementation of an interior point source in the ultra weak variational formulation through source extraction
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
A Plane-Wave Least-Squares Method for Time-Harmonic Maxwell's Equations in Absorbing Media