Yang, Andy L. A novel deep neural network algorithm for the Helmholtz scattering problem in the unbounded domain. (English) Zbl 07793823 Int. J. Numer. Anal. Model. 20, No. 5, 724-738 (2023). MSC: 65L15 34L16 PDFBibTeX XMLCite \textit{A. L. Yang}, Int. J. Numer. Anal. Model. 20, No. 5, 724--738 (2023; Zbl 07793823) Full Text: DOI
Yang, Andy L.; Gu, Feng A mesh-less, ray-based deep neural network method for the Helmholtz equation with high frequency. (English) Zbl 1513.65501 Int. J. Numer. Anal. Model. 19, No. 4, 587-601 (2022). MSC: 65N99 35J05 68T07 PDFBibTeX XMLCite \textit{A. L. Yang} and \textit{F. Gu}, Int. J. Numer. Anal. Model. 19, No. 4, 587--601 (2022; Zbl 1513.65501) Full Text: Link
Chen, Yanping; Lin, Xiuxiu; Huang, Yunqing Error analysis of spectral approximation for space-time fractional optimal control problems with control and state constraints. (English) Zbl 1524.49053 J. Comput. Appl. Math. 413, Article ID 114293, 15 p. (2022). MSC: 49M25 35R11 49J20 26A33 65M15 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 413, Article ID 114293, 15 p. (2022; Zbl 1524.49053) Full Text: DOI
Zhang, Jinling; Chen, Yanping; Huang, Yunqing; Huang, Fenglin A posteriori error estimates for \(hp\) spectral element approximation of elliptic control problems with integral control and state constraints. (English) Zbl 1499.65693 Adv. Appl. Math. Mech. 14, No. 2, 469-493 (2022). MSC: 65N30 35Q93 49K20 49M25 65K10 PDFBibTeX XMLCite \textit{J. Zhang} et al., Adv. Appl. Math. Mech. 14, No. 2, 469--493 (2022; Zbl 1499.65693) Full Text: DOI
Hong, Youngjoon; Nicholls, David A rigorous numerical analysis of the transformed field expansion method for diffraction by periodic, layered structures. (English) Zbl 1466.65212 SIAM J. Numer. Anal. 59, No. 1, 456-476 (2021). Reviewer: Andreas Kleefeld (Jülich) MSC: 65N35 78A45 78A48 35Q60 78M22 PDFBibTeX XMLCite \textit{Y. Hong} and \textit{D. Nicholls}, SIAM J. Numer. Anal. 59, No. 1, 456--476 (2021; Zbl 1466.65212) Full Text: DOI
Wu, Tingting; Sun, Yuran; Cheng, Dongsheng A new finite difference scheme for the 3D Helmholtz equation with a preconditioned iterative solver. (English) Zbl 1457.76112 Appl. Numer. Math. 161, 348-371 (2021). MSC: 76M20 76Q05 65N12 PDFBibTeX XMLCite \textit{T. Wu} et al., Appl. Numer. Math. 161, 348--371 (2021; Zbl 1457.76112) Full Text: DOI
Wang, Hao; Yang, Wei; Huang, Yunqing Adaptive finite element method for the sound wave problems in two kinds of media. (English) Zbl 1443.65224 Comput. Math. Appl. 79, No. 3, 789-801 (2020). MSC: 65M60 76Q05 PDFBibTeX XMLCite \textit{H. Wang} et al., Comput. Math. Appl. 79, No. 3, 789--801 (2020; Zbl 1443.65224) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing Galerkin spectral approximation of optimal control problems with \(L^2\)-norm control constraint. (English) Zbl 1448.49028 Appl. Numer. Math. 150, 418-432 (2020). MSC: 49K20 65N35 65N15 35J99 PDFBibTeX XMLCite \textit{X. Lin} et al., Appl. Numer. Math. 150, 418--432 (2020; Zbl 1448.49028) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing A posteriori error estimates of \(hp\) spectral element methods for optimal control problems with \(L^2\)-norm state constraint. (English) Zbl 07171736 Numer. Algorithms 83, No. 3, 1145-1169 (2020). MSC: 65-XX PDFBibTeX XMLCite \textit{X. Lin} et al., Numer. Algorithms 83, No. 3, 1145--1169 (2020; Zbl 07171736) Full Text: DOI
Chen, Yanping; Lin, Xiuxiu; Huang, Yunqing; Lin, Qian \(hp\) spectral element approximation for integral state constrained optimal control problems governed by harmonic equations. (English) Zbl 1440.65244 J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020). MSC: 65N35 65N15 65N50 31A30 49K20 93C20 35Q93 35B45 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020; Zbl 1440.65244) Full Text: DOI
Liu, Xiao; Xi, Yuanzhe; Saad, Yousef; de Hoop, Maarten V. Solving the three-dimensional high-frequency Helmholtz equation using contour integration and polynomial preconditioning. (English) Zbl 1434.65234 SIAM J. Matrix Anal. Appl. 41, No. 1, 58-82 (2020). MSC: 65N22 15A06 65F08 65F10 65Y20 PDFBibTeX XMLCite \textit{X. Liu} et al., SIAM J. Matrix Anal. Appl. 41, No. 1, 58--82 (2020; Zbl 1434.65234) Full Text: DOI arXiv
Chen, Yanping; Zhang, Jinling; Huang, Yunqing; Xu, Yeqing A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems. (English) Zbl 1421.35188 Appl. Numer. Math. 144, 42-58 (2019). MSC: 35J99 49J20 PDFBibTeX XMLCite \textit{Y. Chen} et al., Appl. Numer. Math. 144, 42--58 (2019; Zbl 1421.35188) Full Text: DOI
Wang, Kun; Wong, Yau Shu Is pollution effect of finite difference schemes avoidable for multi-dimensional Helmholtz equations with high wave numbers? (English) Zbl 1488.65562 Commun. Comput. Phys. 21, No. 2, 490-514 (2017). MSC: 65N06 65N15 65N22 65F05 35J05 78A50 35Q60 PDFBibTeX XMLCite \textit{K. Wang} and \textit{Y. S. Wong}, Commun. Comput. Phys. 21, No. 2, 490--514 (2017; Zbl 1488.65562) Full Text: DOI
Zhou, Jianwei; Yang, Danping; Liu, Yujie A-posteriori error estimates for uniform \(p\)-version finite element methods in square. (English) Zbl 1488.65682 Adv. Appl. Math. Mech. 9, No. 2, 272-281 (2017). MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{J. Zhou} et al., Adv. Appl. Math. Mech. 9, No. 2, 272--281 (2017; Zbl 1488.65682) Full Text: DOI
Wang, Kun; Wong, Yau Shu; Huang, Jizu Solving Helmholtz equation at high wave numbers in exterior domains. (English) Zbl 1411.78008 Appl. Math. Comput. 298, 221-235 (2017). MSC: 78M20 65N06 65N15 65N22 78A25 PDFBibTeX XMLCite \textit{K. Wang} et al., Appl. Math. Comput. 298, 221--235 (2017; Zbl 1411.78008) Full Text: DOI
Bouche, Daniel; Hong, Youngjoon; Jung, Chang-Yeol Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers. (English) Zbl 1379.78008 Discrete Contin. Dyn. Syst. 37, No. 3, 1159-1181 (2017). Reviewer: Pierluigi Maponi (Camerino) MSC: 78A45 34E20 35B40 78A05 34B30 35J05 78M35 PDFBibTeX XMLCite \textit{D. Bouche} et al., Discrete Contin. Dyn. Syst. 37, No. 3, 1159--1181 (2017; Zbl 1379.78008) Full Text: DOI
Zhang, Chao; Liu, Wenjie; Wang, Li-Lian A new collocation scheme using non-polynomial basis functions. (English) Zbl 1359.65138 J. Sci. Comput. 70, No. 2, 793-818 (2017). MSC: 65L60 65L15 PDFBibTeX XMLCite \textit{C. Zhang} et al., J. Sci. Comput. 70, No. 2, 793--818 (2017; Zbl 1359.65138) Full Text: DOI
Zhang, Jing; Wang, Li-Lian; Li, Huiyuan; Zhang, Zhimin Optimal spectral schemes based on generalized prolate spheroidal wave functions of order \(-1\). (English) Zbl 1359.65139 J. Sci. Comput. 70, No. 2, 451-477 (2017). MSC: 65L60 65L15 PDFBibTeX XMLCite \textit{J. Zhang} et al., J. Sci. Comput. 70, No. 2, 451--477 (2017; Zbl 1359.65139) Full Text: DOI
Zhou, Jianwei; Zhang, Juan; Jiang, Ziwu The a posteriori error estimates of Chebyshev-Petrov-Galerkin methods for second-order equations. (English) Zbl 1382.65224 Appl. Math. Lett. 60, 126-134 (2016). MSC: 65L60 65L70 PDFBibTeX XMLCite \textit{J. Zhou} et al., Appl. Math. Lett. 60, 126--134 (2016; Zbl 1382.65224) Full Text: DOI
Baskin, Dean; Spence, Euan A.; Wunsch, Jared Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations. (English) Zbl 1341.35013 SIAM J. Math. Anal. 48, No. 1, 229-267 (2016). Reviewer: Vladimir Mityushev (Kraków) MSC: 35J05 35J25 65N38 78A45 PDFBibTeX XMLCite \textit{D. Baskin} et al., SIAM J. Math. Anal. 48, No. 1, 229--267 (2016; Zbl 1341.35013) Full Text: DOI arXiv
Zhou, Jianwei The a posteriori error estimates for Chebyshev-Galerkin spectral methods in one dimension. (English) Zbl 1488.65698 Adv. Appl. Math. Mech. 7, No. 2, 145-157 (2015). MSC: 65N35 65N30 65N15 35J05 41A50 PDFBibTeX XMLCite \textit{J. Zhou}, Adv. Appl. Math. Mech. 7, No. 2, 145--157 (2015; Zbl 1488.65698) Full Text: DOI
Chen, Yanping; Zhou, Jianwei Error estimates of spectral Legendre-Galerkin methods for the fourth-order equation in one dimension. (English) Zbl 1410.65281 Appl. Math. Comput. 268, 1217-1226 (2015). MSC: 65L60 65L10 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{J. Zhou}, Appl. Math. Comput. 268, 1217--1226 (2015; Zbl 1410.65281) Full Text: DOI
Du, Kui; Li, Buyang; Sun, Weiwei A numerical study on the stability of a class of Helmholtz problems. (English) Zbl 1351.78038 J. Comput. Phys. 287, 46-59 (2015). MSC: 78M10 65N30 65N12 78A25 PDFBibTeX XMLCite \textit{K. Du} et al., J. Comput. Phys. 287, 46--59 (2015; Zbl 1351.78038) Full Text: DOI
Wang, Kun; Wong, Yau Shu Pollution-free finite difference schemes for non-homogeneous Helmholtz equation. (English) Zbl 1499.65614 Int. J. Numer. Anal. Model. 11, No. 4, 787-815 (2014). MSC: 65N06 65N15 65N22 65N12 41A58 35J05 PDFBibTeX XMLCite \textit{K. Wang} and \textit{Y. S. Wong}, Int. J. Numer. Anal. Model. 11, No. 4, 787--815 (2014; Zbl 1499.65614) Full Text: Link
Martinsson, P. G. A direct solver for variable coefficient elliptic PDEs discretized via a composite spectral collocation method. (English) Zbl 1297.65169 J. Comput. Phys. 242, 460-479 (2013). MSC: 65N35 35J05 65F05 PDFBibTeX XMLCite \textit{P. G. Martinsson}, J. Comput. Phys. 242, 460--479 (2013; Zbl 1297.65169) Full Text: DOI
Wu, Xinming; Chen, Wenbin Error estimates of the finite element method for interior transmission problems. (English) Zbl 1457.65223 J. Sci. Comput. 57, No. 2, 331-348 (2013). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{X. Wu} and \textit{W. Chen}, J. Sci. Comput. 57, No. 2, 331--348 (2013; Zbl 1457.65223) Full Text: DOI
Gupta, Praveen Kumar; Yildirim, A.; Rai, K. N. Application of He’s homotopy perturbation method for multi-dimensional fractional Helmholtz equation. (English) Zbl 1357.65189 Int. J. Numer. Methods Heat Fluid Flow 22, No. 4, 424-435 (2012). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{P. K. Gupta} et al., Int. J. Numer. Methods Heat Fluid Flow 22, No. 4, 424--435 (2012; Zbl 1357.65189) Full Text: DOI
Cheng, Pan; Huang, Jin; Wang, Zhu Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations. (English) Zbl 1238.35016 Appl. Math. Mech., Engl. Ed. 32, No. 12, 1505-1514 (2011). Reviewer: Andreas Kleefeld (Cottbus) MSC: 35J05 65N38 65R20 65L06 PDFBibTeX XMLCite \textit{P. Cheng} et al., Appl. Math. Mech., Engl. Ed. 32, No. 12, 1505--1514 (2011; Zbl 1238.35016) Full Text: DOI
Shen, Jie; Wang, Li-Lian On spectral approximations in elliptical geometries using Mathieu functions. (English) Zbl 1198.65236 Math. Comput. 78, No. 266, 815-844 (2009). MSC: 65N35 65N22 65F05 35J05 PDFBibTeX XMLCite \textit{J. Shen} and \textit{L.-L. Wang}, Math. Comput. 78, No. 266, 815--844 (2009; Zbl 1198.65236) Full Text: DOI
Rong, Zhijian; Xu, Chuanju Numerical approximation of acoustic waves by spectral element methods. (English) Zbl 1139.76043 Appl. Numer. Math. 58, No. 7, 999-1016 (2008). MSC: 76M22 76Q05 65M15 PDFBibTeX XMLCite \textit{Z. Rong} and \textit{C. Xu}, Appl. Numer. Math. 58, No. 7, 999--1016 (2008; Zbl 1139.76043) Full Text: DOI
Li, Z. C. The Trefftz method for the Helmholtz equation with degeneracy. (English) Zbl 1141.65082 Appl. Numer. Math. 58, No. 2, 131-159 (2008). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N38 65N15 65N12 35J05 PDFBibTeX XMLCite \textit{Z. C. Li}, Appl. Numer. Math. 58, No. 2, 131--159 (2008; Zbl 1141.65082) Full Text: DOI
Fang, Qirong; Nicholls, David P.; Shen, Jie A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. (English) Zbl 1123.76049 J. Comput. Phys. 224, No. 2, 1145-1169 (2007). MSC: 76M25 76Q05 PDFBibTeX XMLCite \textit{Q. Fang} et al., J. Comput. Phys. 224, No. 2, 1145--1169 (2007; Zbl 1123.76049) Full Text: DOI