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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
An optimized CIP-FEM to reduce the pollution errors for the Helmholtz equation on a general unstructured mesh
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
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
A Trefftz method with reconstruction of the normal derivative applied to elliptic equations
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
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
A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger 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
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
Adaptive refinement for hp–Version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
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
Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler Mathematical Models and Methods in Applied Sciences 29(09) 1619 (2019) https://doi.org/10.1142/S0218202519500301
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
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
Numerical Microlocal Analysis by Fast Gaussian Wave Packet Transforms and Application to High-Frequency Helmholtz Problems
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
Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers
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
Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the $$hp$$ h p -Version
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
The method of 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
An Unconditionally Stable Discontinuous Galerkin Method for the Elastic Helmholtz Equations with Large Frequency
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
Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes