FEM-DtN-SIM method for computing resonances of Schrödinger operators.

Jiguang Sun https://orcid.org/0000-0003-4105-8463

Bo Gong Takumi Sato Jiguang Sun Xinming Wu FEM-DtN-SIM method for computing resonances of Schrödinger operators. 109803 2026 173 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2025.109803 db/journals/appml/appml173.html#GongSSW26 streams/journals/appml

Chao Wang Jintao Cui Jiguang Sun A mixed method for Maxwell's transmission eigenvalue problem using H ( curl 2 ) conforming finite elements. 117198 2026 477 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2025.117198 db/journals/jcam/jcam477.html#WangCS26 streams/journals/jcam

Jiayu Han Jiguang Sun Qian Zhang 0050 Error Analysis of a Conforming Finite Element Method for the Modified Electromagnetic Transmission Eigenvalue Problem. 2026 303-325 64 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/25m1723608 db/journals/siamnum/siamnum64.html#HanSZ26 streams/journals/siamnum

Tanxin Zhu Emran Hossen Chen Zhao Michele Esposito Jiguang Sun Weihua Zhou Imaging-Derived Coronary Fractional Flow Reserve: Advances in Physics-Based, Machine-Learning, and Physics-Informed Methods. 2026 February abs/2602.16000 CoRR https://doi.org/10.48550/arXiv.2602.16000 db/journals/corr/corr2602.html#abs-2602-16000 streams/journals/corr

Bo Gong Takumi Sato Jiguang Sun Xinming Wu Edge element DtN method for electromagnetic scattering poles of perfectly conducting obstacles. 2026 March abs/2603.14708 CoRR https://doi.org/10.48550/arXiv.2603.14708 db/journals/corr/corr2603.html#abs-2603-14708 streams/journals/corr

Bo Gong Jiguang Sun Spurious-mode-free finite element method for scattering resonances in transmission problems. 2026 April abs/2604.14539 CoRR https://doi.org/10.48550/arXiv.2604.14539 db/journals/corr/corr2604.html#abs-2604-14539 streams/journals/corr

Bo Gong Takumi Sato Jiguang Sun Xinming Wu FEM-DtN-SIM Method for Computing Resonances of Schrödinger Operators. 2025 April abs/2504.11680 CoRR https://doi.org/10.48550/arXiv.2504.11680 db/journals/corr/corr2504.html#abs-2504-11680 streams/journals/corr

Haoqian Li Jiguang Sun Zhiwen Zhang 0001 Operator Inference for Elliptic Eigenvalue Problems. 2025 April abs/2504.15733 CoRR https://doi.org/10.48550/arXiv.2504.15733 db/journals/corr/corr2504.html#abs-2504-15733 streams/journals/corr

Xiaodong Liu 0020 Jiguang Sun Lei Zhang Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles. 2025 July abs/2507.04242 CoRR https://doi.org/10.48550/arXiv.2507.04242 db/journals/corr/corr2507.html#abs-2507-04242 streams/journals/corr

Yunyun Ma Jiguang Sun Fourier-Galerkin method for scattering poles of sound soft obstacles. 2025 October abs/2510.03826 CoRR https://doi.org/10.48550/arXiv.2510.03826 db/journals/corr/corr2510.html#abs-2510-03826 streams/journals/corr

Yingxia Xi Junshan Lin Jiguang Sun A finite element contour integral method for computing the resonances of metallic grating structures with subwavelength holes. 161-171 2024 170 Comput. Math. Appl. https://doi.org/10.1016/j.camwa.2024.06.022 db/journals/cma/cma170.html#XiLS24 streams/journals/cma

Zhongyuan Chen Jiguang Sun Jianlin Xia A Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection. 48 2024 August 100 J. Sci. Comput. 2 https://doi.org/10.1007/s10915-024-02599-x db/journals/jscic/jscic100.html#ChenSX24 streams/journals/jscic

Yingxia Xi Junshan Lin Jiguang Sun A finite element contour integral method for computing the resonances of metallic grating structures with subwavelength holes. 2024 abs/2403.04514 CoRR https://doi.org/10.48550/arXiv.2403.04514 db/journals/corr/corr2403.html#abs-2403-04514

Yingxia Xi Bo Gong Jiguang Sun Analysis of a finite element DtN method for scattering resonances of sound hard obstacles. 2024 abs/2404.09300 CoRR https://doi.org/10.48550/arXiv.2404.09300 db/journals/corr/corr2404.html#abs-2404-09300

Yunyun Ma Jiguang Sun Computation of scattering poles using boundary integrals. 108792 2023 December 146 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2023.108792 db/journals/appml/appml146.html#MaS23

Yunyun Ma Jiguang Sun Analysis of a Fourier-Galerkin Method for the Transmission Eigenvalue Problem based on a Boundary Integral Formulation. 60 2023 May 95 J. Sci. Comput. 2 https://doi.org/10.1007/s10915-023-02197-3 db/journals/jscic/jscic95.html#MaS23

Yingxia Xi Jiguang Sun Parallel Multi-step Spectral Indicator Method for Nonlinear Eigenvalue Problems. 2023 abs/2312.13117 CoRR https://doi.org/10.48550/arXiv.2312.13117 db/journals/corr/corr2312.html#abs-2312-13117

Kaibo Hu Jiguang Sun Qian Zhang 0050 Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes. 2023 abs/2312.13425 CoRR https://doi.org/10.48550/arXiv.2312.13425 db/journals/corr/corr2312.html#abs-2312-13425

Jiguang Sun Local estimators and Bayesian inverse problems with non-unique solutions. 108149 2022 132 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2022.108149 db/journals/appml/appml132.html#Sun22

Xiangying Pang Jiguang Sun Zhimin Zhang 0002 FE-holomorphic operator function method for nonlinear plate vibrations with elastically added masses. 114156 2022 410 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2022.114156 https://www.wikidata.org/entity/Q114201896 db/journals/jcam/jcam410.html#PangSZ22

Bo Gong Jiguang Sun Tiara Turner Chunxiong Zheng Finite element/holomorphic operator function method for the transmission eigenvalue problem. 2517-2537 2022 91 Math. Comput. 338 https://doi.org/10.1090/mcom/3767 https://www.wikidata.org/entity/Q114094300 db/journals/moc/moc91.html#GongSTZ22

Jiguang Sun Regular Convergence and Finite Element Methods for Eigenvalue Problems. 2022 abs/2206.00626 CoRR https://doi.org/10.48550/arXiv.2206.00626 db/journals/corr/corr2206.html#abs-2206-00626

Yanfang Liu Zhizhang Wu Jiguang Sun Zhiwen Zhang 0001 Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data. 2022 abs/2209.08222 CoRR https://doi.org/10.48550/arXiv.2209.08222 db/journals/corr/corr2209.html#abs-2209-08222

Wenqiang Xiao Bo Gong Jiguang Sun Zhimin Zhang 0002 Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials. 27 2021 87 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-021-01439-6 db/journals/jscic/jscic87.html#XiaoGSZ21

Bo Gong Jiguang Sun Xinming Wu Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues. 2430-2448 2021 59 SIAM J. Numer. Anal. 5 https://doi.org/10.1137/20M1328889 db/journals/siamnum/siamnum59.html#GongSW21

Zhaoxing Li Yanfang Liu Jiguang Sun Liwei Xu Quality-Bayesian Approach to Inverse Acoustic Source Problems with Partial Data. A1062-A1080 2021 43 SIAM J. Sci. Comput. 2 https://doi.org/10.1137/20M132345X db/journals/siamsc/siamsc43.html#LiLSX21

Yanfang Liu Yukun Guo Jiguang Sun A deterministic-statistical approach to reconstruct moving sources using sparse partial data. 2021 abs/2101.01290 CoRR https://arxiv.org/abs/2101.01290 db/journals/corr/corr2101.html#abs-2101-01290

Xiangying Pang Jiguang Sun Zhimin Zhang 0002 FE-Holomorphic Operator Function Method for Nonlinear Plate Vibrations with Elastically Added Masses. 2021 abs/2108.03681 CoRR https://arxiv.org/abs/2108.03681 db/journals/corr/corr2108.html#abs-2108-03681

Wenqiang Xiao Bo Gong Jiguang Sun Zhimin Zhang 0002 A new finite element approach for the Dirichlet eigenvalue problem. 106295 2020 105 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2020.106295 db/journals/appml/appml105.html#XiaoGSZ20

Zhaoxing Li Zhiliang Deng Jiguang Sun Extended-Sampling-Bayesian Method for Limited Aperture Inverse Scattering Problems. 422-444 2020 13 SIAM J. Imaging Sci. 1 https://doi.org/10.1137/19M1270501 db/journals/siamis/siamis13.html#LiDS20

Wenqiang Xiao Bo Gong Jiguang Sun Zhimin Zhang 0002 A new finite element approach for the Dirichlet eigenvalue problem. 2020 abs/2001.05332 CoRR https://arxiv.org/abs/2001.05332 db/journals/corr/corr2001.html#abs-2001-05332

Bo Gong Jiguang Sun Tiara Turner Chunxiong Zheng Finite Element Approximation of Transmission Eigenvalues for Anisotropic Media. 2020 abs/2001.05340 CoRR https://arxiv.org/abs/2001.05340 db/journals/corr/corr2001.html#abs-2001-05340

Bo Gong Jiguang Sun Xinming Wu Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues. 2020 abs/2004.04588 CoRR https://arxiv.org/abs/2004.04588 db/journals/corr/corr2004.html#abs-2004-04588

Zhaoxing Li Yanfang Liu Jiguang Sun Liwei Xu Quality-Bayesian approach to inverse acoustic source problems with partial data. 2020 abs/2004.04609 CoRR https://arxiv.org/abs/2004.04609 db/journals/corr/corr2004.html#abs-2004-04609

Ruihao Huang Jiguang Sun Chao Yang A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices. 2020 abs/2006.16117 CoRR https://arxiv.org/abs/2006.16117 db/journals/corr/corr2006.html#abs-2006-16117

Lixiu Wang Qian Zhang 0050 Jiguang Sun Zhimin Zhang 0002 A priori and a posteriori error estimates for the quad-curl eigenvalue problem. 2020 abs/2007.01330 CoRR https://arxiv.org/abs/2007.01330 db/journals/corr/corr2007.html#abs-2007-01330

Wenqiang Xiao Bo Gong Jiguang Sun Zhimin Zhang 0002 Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials. 2020 abs/2007.11540 CoRR https://arxiv.org/abs/2007.11540 db/journals/corr/corr2007.html#abs-2007-11540

Wenqiang Xiao Jiguang Sun A Novel Computational Method for Band Structures of Dispersive Photonic Crystals. 2020 abs/2010.01603 CoRR https://arxiv.org/abs/2010.01603 db/journals/corr/corr2010.html#abs-2010-01603

Zhaoxing Li Jiguang Sun Liwei Xu An extended sampling-ensemble Kalman filter approach for partial data inverse elastic problems. 2020 abs/2010.05753 CoRR https://arxiv.org/abs/2010.05753 db/journals/corr/corr2010.html#abs-2010-05753

Xiaodong Liu 0020 Jiguang Sun Data recovery in inverse scattering: From limited-aperture to full-aperture. 350-364 2019 386 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.10.036 https://www.wikidata.org/entity/Q129078326 db/journals/jcphy/jcphy386.html#LiuS19

Kun Wang 0017 Zhaofa Zeng Jiguang Sun Through-Wall Detection of the Moving Paths and Vital Signs of Human Beings. 717-721 2019 16 IEEE Geosci. Remote. Sens. Lett. 5 https://doi.org/10.1109/LGRS.2018.2881311 https://www.wikidata.org/entity/Q128893928 db/journals/lgrs/lgrs16.html#WangZS19

Sebastián Domínguez Nilima Nigam Jiguang Sun Revisiting the Jones Eigenproblem in Fluid-Structure Interaction. 2385-2408 2019 79 SIAM J. Appl. Math. 6 https://doi.org/10.1137/18M1198235 https://www.wikidata.org/entity/Q126575458 db/journals/siamam/siamam79.html#DominguezNS19

Juan Liu Xiaodong Liu 0020 Jiguang Sun Extended Sampling Method for Inverse Elastic Scattering Problems Using One Incident Wave. 874-892 2019 12 SIAM J. Imaging Sci. 2 https://doi.org/10.1137/19M1237788 db/journals/siamis/siamis12.html#LiuLS19

Ruihao Huang Jiguang Sun Chao Yang Recursive integral method with Cayley transformation. 2018 25 Numer. Linear Algebra Appl. 6 https://doi.org/10.1002/nla.2199 https://www.wikidata.org/entity/Q129564038 db/journals/nla/nla25.html#HuangSY18

Constantin Bacuta Fioralba Cakoni Houssem Haddar Jiguang Sun Proceedings of the international conference on computational mathematics and inverse problems honoring Peter Monk. 2639 2017 74 Comput. Math. Appl. 11 https://doi.org/10.1016/j.camwa.2017.09.001 db/journals/cma/cma74.html#BacutaCHS17

Ruming Zhang Jiguang Sun Chunxiong Zheng Reconstruction of a penetrable obstacle in periodic waveguides. 2739-2751 2017 74 Comput. Math. Appl. 11 https://doi.org/10.1016/j.camwa.2017.08.028 db/journals/cma/cma74.html#ZhangSZ17

Susanne C. Brenner Jiguang Sun Li-Yeng Sung Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains. 495-513 2017 73 J. Sci. Comput. 2-3 https://doi.org/10.1007/s10915-017-0449-0 db/journals/jscic/jscic73.html#BrennerSS17

Ruihao Huang Allan A. Struthers Jiguang Sun Ruming Zhang Recursive integral method for transmission eigenvalues. 830-840 2016 327 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2016.10.001 db/journals/jcphy/jcphy327.html#HuangSSZ16

Hongrui Geng Xia Ji 0001 Jiguang Sun Liwei Xu C<sup>0</sup> IP Methods for the Transmission Eigenvalue Problem. 326-338 2016 68 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-015-0140-2 db/journals/jscic/jscic68.html#GengJSX16

Jiguang Sun A mixed FEM for the quad-curl eigenvalue problem. 185-200 2016 132 Numerische Mathematik 1 https://doi.org/10.1007/s00211-015-0708-7 db/journals/nm/nm132.html#Sun16

Ruming Zhang Jiguang Sun Efficient finite element method for grating profile reconstruction. 405-419 2015 302 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2015.09.016 db/journals/jcphy/jcphy302.html#ZhangS15

Xia Ji 0001 Jiguang Sun Yang Yang 0014 Optimal penalty parameter for C<sup>0</sup> IPDG. 112-117 2014 37 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2014.06.001 db/journals/appml/appml37.html#JiSY14

Fioralba Cakoni Peter Monk 0001 Jiguang Sun Error Analysis for the Finite Element Approximation of Transmission Eigenvalues. 419-427 2014 14 Comput. Methods Appl. Math. 4 https://doi.org/10.1515/cmam-2014-0021 db/journals/cmam/cmam14.html#CakoniMS14

Xia Ji 0001 Jiguang Sun Hehu Xie A Multigrid Method for Helmholtz Transmission Eigenvalue Problems. 276-294 2014 60 J. Sci. Comput. 2 https://doi.org/10.1007/s10915-013-9794-9 db/journals/jscic/jscic60.html#JiSX14

Xia Ji 0001 Jiguang Sun A multi-level method for transmission eigenvalues of anisotropic media. 422-435 2013 255 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2013.08.030 db/journals/jcphy/jcphy255.html#JiS13

Jing Li 0005 Zhaofa Zeng Jiguang Sun Fengshan Liu Through-Wall Detection of Human Being's Movement by UWB Radar. 1079-1083 2012 9 IEEE Geosci. Remote. Sens. Lett. 6 https://doi.org/10.1109/LGRS.2012.2190707 db/journals/lgrs/lgrs9.html#LiZSL12

Peter Monk 0001 Jiguang Sun Finite Element Methods for Maxwell's Transmission Eigenvalues. 2012 34 SIAM J. Sci. Comput. 3 https://doi.org/10.1137/110839990 db/journals/siamsc/siamsc34.html#MonkS12

Xia Ji 0001 Jiguang Sun Tiara Turner Algorithm 922: A Mixed Finite Element Method for Helmholtz Transmission Eigenvalues. 29:1-29:8 2012 38 ACM Trans. Math. Softw. 4 https://doi.org/10.1145/2331130.2331137 https://www.wikidata.org/entity/Q113310372 db/journals/toms/toms38.html#JiST12

George C. Hsiao Fengshan Liu Jiguang Sun Liwei Xu A coupled BEM and FEM for the interior transmission problem in acoustics. 5213-5221 2011 235 J. Comput. Appl. Math. 17 https://doi.org/10.1016/j.cam.2011.05.011 db/journals/jcam/jcam235.html#HsiaoLSX11

Jiguang Sun Iterative Methods for Transmission Eigenvalues. 1860-1874 2011 49 SIAM J. Numer. Anal. 5 https://doi.org/10.1137/100785478 db/journals/siamnum/siamnum49.html#Sun11

Zhaofa Zeng Jiguang Sun Jing Li 0005 Fengshan Liu Qi Lu Xiong Chen The analysis of TWI data for human being's periodic motions. 862-865 2011 IGARSS https://doi.org/10.1109/IGARSS.2011.6049267 conf/igarss/2011 db/conf/igarss/igarss2011.html#ZengSLLLC11

Wei Cai Xia Ji 0001 Jiguang Sun Sihong Shao A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media. 9933-9954 2008 227 J. Comput. Phys. 23 https://doi.org/10.1016/j.jcp.2008.08.012 db/journals/jcphy/jcphy227.html#CaiJSS08

Jiguang Sun Backward errors for the inverse eigenvalue problem. 339-349 1999 82 Numerische Mathematik 2 https://doi.org/10.1007/s002110050422 db/journals/nm/nm82.html#Sun99

Constantin Bacuta Susanne C. Brenner Wei Cai Fioralba Cakoni Xiong Chen Zhongyuan Chen Jintao Cui Zhiliang Deng Sebastián Domínguez Michele Esposito Hongrui Geng Bo Gong Yukun Guo Houssem Haddar Jiayu Han Emran Hossen George C. Hsiao Kaibo Hu Ruihao Huang Xia Ji 0001 Haoqian Li Jing Li 0005 Zhaoxing Li Junshan Lin Fengshan Liu Juan Liu Xiaodong Liu 0020 Yanfang Liu Qi Lu Yunyun Ma Peter Monk 0001 Nilima Nigam Xiangying Pang Takumi Sato Sihong Shao Allan A. Struthers Li-Yeng Sung Tiara Turner Chao Wang Kun Wang 0017 Lixiu Wang Xinming Wu Zhizhang Wu Yingxia Xi Jianlin Xia Wenqiang Xiao Hehu Xie Liwei Xu Chao Yang Yang Yang 0014 Zhaofa Zeng Lei Zhang Qian Zhang 0050 Ruming Zhang Zhimin Zhang 0002 Zhiwen Zhang 0001 Chen Zhao Chunxiong Zheng Weihua Zhou Tanxin Zhu