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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations

As of 19 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2511.13217.

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2511.13217 v2

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measured 54 of 54 reference resolution

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54 of 54 outbound references displayed

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Outbound references

Observation 4287f329-fc00-4621-86a4-90d05b8d7bb2 · outbound

This paper cites Coupled mode and finite element approximations of underwater sound propagation prob- lems in general stratified environments.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Coupled mode and finite element approximations of underwater sound propagation prob- lems in general stratified environments

Reference 1

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Observation 693c5cea-4bfa-48ed-800d-a3d06087201b · outbound

This paper cites A two point boundary value problem with a rapidly oscillating solution.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A two point boundary value problem with a rapidly oscillating solution

Reference 2

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Observation 8ae8f424-257b-42c0-8cb0-7715582511b8 · outbound

This paper cites Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?

Reference 3

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Observation 5f4b219d-776d-4b5a-86bd-6be9e8d66834 · outbound

This paper cites On accuracy conditions for the numerical compu- tation of waves.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On accuracy conditions for the numerical compu- tation of waves

Reference 4

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Observation b79ff9b4-6f54-4e29-a319-5c4828e70801 · outbound

This paper cites A space–time continuous and coercive formulation for the wave equation.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A space–time continuous and coercive formulation for the wave equation

Reference 5

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Observation 2471ba1b-27b6-4584-8e81-ecc5c2745d0a · outbound

This paper cites Wave-number-explicit bounds in time-harmonic scat- tering.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Wave-number-explicit bounds in time-harmonic scat- tering

Reference 6

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Observation e56208c7-aba7-41ab-9139-d4186295a3f2 · outbound

This paper cites The virial theorem and the method of multipliers in spectral theory.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations The virial theorem and the method of multipliers in spectral theory

Reference 7

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Observation bea4ee2f-0cba-4028-8866-b3e01549ca1f · outbound

This paper cites An efficient neural network method with plane wave activa- tion functions for solving Helmholtz equation.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An efficient neural network method with plane wave activa- tion functions for solving Helmholtz equation

Reference 8

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Observation 98b3239b-3b83-4edc-b361-b54131815303 · outbound

This paper cites Sharp regularity coefficient estimates for complex-valued acous- tic and elastic Helmholtz equations.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Sharp regularity coefficient estimates for complex-valued acous- tic and elastic Helmholtz equations

Reference 9

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Observation 8968cc2b-70cc-4c85-b168-81bbb3b846c7 · outbound

This paper cites Evolution equations on non-flat waveguides.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Evolution equations on non-flat waveguides

Reference 10

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Observation 1c04cfa0-58e8-4c66-9db5-d9d1f4c9dfb6 · outbound

This paper cites Dautray and J.-L.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Dautray and J.-L

Reference 11

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Observation 9c97befe-daec-47ee-ac5a-f477500da86a · outbound

This paper cites Frequency domain treatment of one-dimensional scalar waves.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Frequency domain treatment of one-dimensional scalar waves

Reference 12

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work

Reference 13

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Observation 99a870b8-5a11-4f28-b961-c56b670e60e3 · outbound

This paper cites hp-discontinuous Galerkin methods for the Helmholtz equation with large wave number.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations hp-discontinuous Galerkin methods for the Helmholtz equation with large wave number

Reference 14

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Observation 575e771a-adb3-4b95-96b0-0736de8ace0f · outbound

This paper cites Variational methods for underwater acoustic problems.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Variational methods for underwater acoustic problems

Reference 15

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Observation e1fbf4fa-bfbb-4e71-842e-1e4a415a6d41 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work

Reference 16

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Observation 3455eeee-db77-45e0-9067-da7e58b3268b · outbound

This paper cites Givoli.Numerical methods for problems in infinite domains.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Givoli.Numerical methods for problems in infinite domains

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Observation b6a18e0e-f688-467d-92c2-15085aa2e8c3 · outbound

This paper cites A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains

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Observation 433e01d8-272c-41f5-b4c7-50fc4dff89b2 · outbound

This paper cites Stability and finite element error analysis for the Helmholtz equa- tion with variable coefficients.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Stability and finite element error analysis for the Helmholtz equa- tion with variable coefficients

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Observation 04d07d74-5f28-4516-b6e7-b0657f60bf2a · outbound

This paper cites Grisvard.Elliptic problems in nonsmooth domains.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Grisvard.Elliptic problems in nonsmooth domains

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Observation 7a50dd62-fdf5-4b28-ac24-1abe2ca4300f · outbound

This paper cites On controllability methods for the Helmholtz equation.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On controllability methods for the Helmholtz equation

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Observation 48bca2ab-0d65-4923-b93a-aa6a9950ee55 · outbound

This paper cites Wave decay for star-shaped obstacles inR 3: papers of Morawetz and Ralston revisited.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Wave decay for star-shaped obstacles inR 3: papers of Morawetz and Ralston revisited

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Observation 37fc9bcd-9b1b-4941-92df-614746d2b2b3 · outbound

This paper cites A survey of Trefftz methods for the Helmholtz equation.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A survey of Trefftz methods for the Helmholtz equation

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Observation 7f53bd6a-3209-4706-9b05-f3f8b1bd5892 · outbound

This paper cites Ihlenburg.Finite Element Analysis of Acoustic Scattering.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Ihlenburg.Finite Element Analysis of Acoustic Scattering

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Observation cbb4e0ce-7511-4511-89ef-2e4ec30ce2d5 · outbound

This paper cites Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM

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Observation bd266947-3c15-4ae6-ac2a-48fae9ad5a5b · outbound

This paper cites Exact non-reflecting boundary conditions.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Exact non-reflecting boundary conditions

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Observation 9170222c-43d8-466c-a6e0-7d1fd16793e9 · outbound

This paper cites Lanczos.The Variational Principles of Mechanics.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Lanczos.The Variational Principles of Mechanics

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Observation 646e9611-807d-40db-98dc-f45cb1b780d5 · outbound

This paper cites Nonlinear wave equations in infinite waveguides.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Nonlinear wave equations in infinite waveguides

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Observation aa7688f3-7501-490f-8764-576389f4e9b2 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Lions and E

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Observation a06fd295-09a3-4568-883a-2102783450a6 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations DeepXDE: a deep learning library for solving differential equations

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Observation 85686a09-3d2c-46ae-9e42-0559cf6665e6 · outbound

This paper cites Analysis and finite element methods for a fluid- solid interaction problem in one dimension.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Analysis and finite element methods for a fluid- solid interaction problem in one dimension

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Observation b35892b2-ba4b-4c3b-b04e-2c2085a3010c · outbound

This paper cites Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions

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Observation 4f1b75fa-f153-40b8-98cd-efb46128ae74 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On Generalized Finite Element Methods

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Observation 14e38eb7-a9e1-4471-9688-394f7fd568ef · outbound

This paper cites Nonlinear hyperbolic equations in infinite homo- geneous waveguides.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Nonlinear hyperbolic equations in infinite homo- geneous waveguides

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Observation 5e26a371-98cb-413f-a80a-486198efdc85 · outbound

This paper cites Near- and far-field boundary conditions for a finite element method for the Helmholtz equation in axisymmetric problems of underwater acoustics.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Near- and far-field boundary conditions for a finite element method for the Helmholtz equation in axisymmetric problems of underwater acoustics

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Observation 4fbc994d-7330-436c-ad38-0636c3c0ad32 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Helmholtz equation with artificial boundary conditions in a two-dimensional waveguide

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Observation 5dc622ce-15d5-48da-9048-222539b8d924 · outbound

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A finite element method with nonlocal boundary condi- tions for the Helmholtz equation with complex wavenumber in stratified waveguides

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This paper cites Is the Helmholtz Equation Really Sign-Indefinite?.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Is the Helmholtz Equation Really Sign-Indefinite?

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work

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This paper cites An inequality for the reduced wave operator and the jus- tification of geometrical optics.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An inequality for the reduced wave operator and the jus- tification of geometrical optics

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On the modes of decay for the wave equation in the exterior of a reflecting body

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This paper cites Morrey–Campanato estimates for Helmholtz equations.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Morrey–Campanato estimates for Helmholtz equations

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Eliminating the pollution effect in Helmholtz problems by local subscale cor- rection

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This paper cites Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A refined finite element convergence theory for highly indefinite Helmholtz problems

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Stability estimate for the Helmholtz equation with rapidly jumping coefficients

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Feasibility study on solving the Helmholtz equation in 3D with PINNs

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A perfectly matched layer for the Helmholtz equation in a semi- infinite strip

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A versatile framework to solve the Helmholtz equation using physics-informed neural networks

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A new frequency- uniform coercive boundary integral equation for acoustic scattering

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Morawetz inequalities

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This paper cites Tao.Nonlinear dispersive equations.

Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Tao.Nonlinear dispersive equations

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Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work

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