Julius Fergy Tiongson Rabago

About

Hello! I'm Fergy. I am a Specially Appointed Assistant Professor at the Faculty of Mathematics and Physics, Kanazawa University. From November 2024 to October 2026, I was a JSPS Postdoctoral Fellow mentored by Professor Masato Kimura. Before that, I was a Postdoctoral Researcher working with Professor Hirofumi Notsu at the same faculty. I also served as an Adjunct Assistant Professor at Temple University, Japan Campus from January to October 2024.

My current research interests include stationary free boundary and free surface problems, moving boundary problems, geometric inverse problems, and applications of shape and topology optimization methods.

Email · Google Scholar · ResearchGate · ORCID · Scopus · researchmap

News

• 2026.09.14 New
  35th Workshop on Mathematical Analysis for Nonlinear Phenomena
• 2026.08.30
  Our paper on theoretical and numerical studies of a Sobolev-gradient coupled complex boundary method for diffusion coefficient reconstruction has been published in The Science Reports of Kanazawa University (with S. P. Nainggolan and H. Notsu).
• 2026.08.24–27
  Mini-symposium on "Recent Advances in Numerical Shape and Topology Optimization Methods: From Theory to Practice" at The 19th SIAM East Asian Section Conference, Jeju Island, 2026 (co-organized with W. Gong and S. Zhu).
• 2026.07.27 (citation details updated: 2026.10.09)
  Our paper on a shape optimization approach for inverse diffusion problems using a single boundary measurement has been published as an Early Access article in Inverse Problems and Imaging (with M. Machida and H. Notsu).
• 2026.07.24
  Young Researchers Workshop on Applied Mathematics @ Kanazawa City, Ishikawa, Japan.
• 2026.06.20–23
  Continuum Mechanics Focusing on Singularities–Numerical Analysis & Scientific Computing 2026 @ Lapu-Lapu City, Cebu, Philippines.
• 2026.05.13 Preprint
  A new paper is up on arXiv on cavity shape reconstruction with a homogeneous Robin condition via a constrained coupled complex boundary method with ADMM, with M. Essahraoui, E. Cherrat, and L. Afraites.
• 2026.04.21 Publication
  Our paper titled "Enhanced shape recovery in advection–diffusion problems via a novel ADMM-based CCBM optimization" has been published in the Journal of Optimization Theory and Applications, Volume 209, Article Number 44, 2026 (with E. Cherrat and L. Afraites).
• 2026.03.04 Preprint
  A new paper is up on arXiv on statistical topological gradient and shape optimization for robust metal–semiconductor contact reconstruction, with L. Afraites, A. Hadri, and M. Hrizi.
• 2026.02.02 Preprint
  A new paper is up on arXiv on numerical methods for diffusion coefficient recovery, with S. P. Nainggolan and H. Notsu.

Education

• PhD Informatics (2020), Nagoya University, Nagoya, Japan, 2017.10 – 2020.09.28
• MSc Mathematics (2017), University of the Philippines Baguio, Baguio City, Philippines, 2015.01 – 2017.01.10
• PMAM Actuarial Science (2015), University of the Philippines Diliman, Quezon City, Philippines, 2011.06 – 2015.01.10
• BSc Mathematics (2010), University of the Philippines Baguio, Baguio City, Philippines, 2007.06 – 2010.10.22

Research

Keywords

• Free boundary problems
• Free surface problems
• Geometric inverse problems
• Moving boundary problems
• Shape optimization methods
• Topology optimization methods

Projects

Novel hybrid methods for accurate shape reconstruction: advancing theory and computational solutions

Development of effective and accurate non-conventional solution methods for shape inverse problems: theory and numerics

The Analysis of Bernoulli free boundary problem using the velocity method and second-order perturbation of identity technique

Journal Refereeing

• Acta Applicandae Mathematicae
• Applied Mathematics and Optimization
• Communications in Nonlinear Science and Numerical Simulation
• Computers & Mathematics with Applications
• Discrete and Continuous Dynamical Systems - S
• Fractional Calculus and Applied Analysis
• International Electronic Journal of Algebra
• International Journal of Computational Fluid Dynamics
• Inverse Problems
• Journal of Optimization Theory and Applications
• Mathematics and Computers in Simulation
• Modern Stochastics: Theory and Applications
• etc.

Papers

Bibliographic listings: MathSciNet · zbMATH

Preprints

M. Essahraoui, E. Cherrat, L. Afraites, and J. F. T. Rabago TBA [PDF] · arXiv · doi

M. Essahraoui, E. Cherrat, L. Afraites, and J. F. T. Rabago Cavity shape reconstruction with a homogeneous Robin condition via a constrained coupled complex boundary method with ADMM (in revision) [PDF] · arXiv:2605.12202

L. Afraites, A. Hadri, M. Hrizi, and J. F. T. Rabago Statistical topological gradient and shape optimization for robust metal–semiconductor contact reconstruction (in revision) [PDF] · arXiv:2603.04216

Selected Publications

S. P. Nainggolan, J. F. T. Rabago, and H. Notsu Theoretical and numerical studies of a Sobolev-gradient coupled complex boundary method for diffusion coefficient reconstruction The Science Reports of Kanazawa University, 69 (2026), 47–71. [PDF] · arXiv:2602.01656

M. Machida, H. Notsu, and J. F. T. Rabago Shape optimization for piecewise parameter identification in inverse diffusion problems with a single boundary measurement Inverse Problems and Imaging, 29 (2027), 181–226. [PDF] · arXiv:2503.14764 · doi:10.3934/ipi.2026049

E. Cherrat, L. Afraites, and J. F. T. Rabago Enhanced shape recovery in advection–diffusion problems via a novel ADMM-based CCBM optimization Journal of Optimization Theory and Applications, 209 (2026), Art. 44, 28 pp. [PDF] · arXiv:2508.16898 · doi:10.1007/s10957-026-02989-1

J. F. T. Rabago and M. Kimura On the well-posedness of a Hele-Shaw-like system resulting from an inverse geometry problem formulated through a shape optimization setting ESAIM: Control, Optimisation and Calculus of Variations, 31 (2025), Art. 64, 65 pp. [PDF] · arXiv:2407.03083 · doi:10.1051/cocv/2025052

E. Cherrat, L. Afraites, and J. F. T. Rabago Numerical solution by shape optimization method to an inverse shape problem in multi-dimensional advection-diffusion problem with space dependent coefficients Applied Mathematics and Optimization, 92 (2025), Art. 13, 44 pp. [PDF] · arXiv:2504.07796 · doi:10.1007/s00245-025-10290-2

J. F. T. Rabago Localization of tumor through a non-conventional numerical shape optimization technique Applied Numerical Mathematics, 217 (2025), 135–171. [PDF] · arXiv:2502.20656 · doi:10.1016/j.apnum.2025.06.005

M. Essahraoui, E. Cherrat, L. Afraites, and J. F. T. Rabago Simultaneous recovery of a corroded boundary and admittance using the Kohn-Vogelius method In Computational Methods for Inverse Problems and Applications, ICMDS 2024, Khouribga, Morocco, October 21–22, 2024, Springer Proc. Math. Stat., vol. 498, Springer, Cham, 2025, 73–89. [PDF] · arXiv:2506.17938 · doi:10.1007/978-3-031-89498-5_6

J. F. T. Rabago, L. Afraites, and H. Notsu Detecting immersed obstacle in Stokes fluid flow using the coupled complex boundary method SIAM Journal on Control and Optimization, 63 (2025), no. 2, 822–851. arXiv:2403.11819 · doi:10.1137/24M1647369

J. F. T. Rabago, A. Hadri, L. Afraites, A. S. Hendy, and M. A. Zaky A robust alternating direction method of multipliers numerical scheme for solving geometric inverse problems in a shape optimization setting Computers & Mathematics with Applications, 175 (2024), 19–32. arXiv:2301.10355 · doi:10.1016/j.camwa.2024.08.034

L. Afraites and J. F. T. Rabago Boundary shape reconstruction with Robin condition: existence result, stability analysis, and inversion via multiple measurements Computational and Applied Mathematics, 43 (2024), Art. 270, 37 pp. [PDF] · arXiv:2404.05202 · doi:10.1007/s40314-024-02741-3

Y. Sunayama, M. Kimura, and J. F. T. Rabago Comoving mesh method for multi-dimensional moving boundary problems: mean-curvature flow and Stefan problems Mathematics and Computers in Simulation, 221 (2024), 589–605. [PDF] · doi:10.1016/j.matcom.2024.03.020

J. F. T. Rabago and H. Notsu Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization settings Applied Mathematics and Optimization, 89 (2024), Art. 2, 56 pp. [PDF] · doi:10.1007/s00245-023-10065-7

E. Cherrat, L. Afraites, and J. F. T. Rabago Shape reconstruction for advection-diffusion problems by shape optimization method: the case of constant velocity Discrete and Continuous Dynamical Systems Series S, 18 (2025), no. 1, 296–320. [PDF] · doi:10.3934/dcdss.2023186

L. Afraites and J. F. T. Rabago Shape optimization methods for detecting an unknown boundary with the Robin condition by a single measurement Discrete and Continuous Dynamical Systems Series S, 18 (2025), no. 1, 43–76. [PDF] · doi:10.3934/dcdss.2022196

J. F. T. Rabago Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions Numerical Algorithms, 94 (2023), 175–227. [PDF] · doi:10.1007/s11075-023-01497-x

J. F. T. Rabago On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems Mathematical Control and Related Fields, 13 (2023), no. 4, 1362–1398. [PDF] · doi:10.3934/mcrf.2022041

Y. Sunayama, J. F. T. Rabago, and M. Kimura Comoving mesh method for certain classes of moving boundary problems Japan Journal of Industrial and Applied Mathematics, 39 (2022), 973–1001. [PDF] · doi:10.1007/s13160-022-00524-z

J. F. T. Rabago and H. Azegami A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional Computational Optimization and Applications, 77 (2020), 251–305. [PDF] · doi:10.1007/s10589-020-00199-7

J. F. T. Rabago and H. Azegami A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem Evolution Equations and Control Theory, 8 (2019), no. 4, 785–824. [PDF] · doi:10.3934/eect.2019038

J. F. T. Rabago and H. Azegami An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data Journal of Engineering Mathematics, 117 (2019), no. 1, 1–29. [PDF] · doi:10.1007/s10665-019-10005-x

J. F. T. Rabago and H. Azegami Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement Japan Journal of Industrial and Applied Mathematics, 36 (2018), no. 1, 131–176. [PDF] · doi:10.1007/s13160-018-0337-5

J. F. T. Rabago and J. B. Bacani Shape optimization approach for solving the Bernoulli problem by tracking the Neumann data: a Lagrangian formulation Communications in Pure & Applied Analysis, 17 (2018), no. 6, 2683–2702. [PDF] · doi:10.3934/cpaa.2018127

J. F. T. Rabago and J. B. Bacani Shape optimization approach to the Bernoulli problem: a Lagrangian formulation IAENG International Journal of Applied Mathematics, 47 (2017), no. 4, 417–424. [PDF]

J. B. Bacani and J. F. T. Rabago On the second-order shape derivative of the Kohn-Vogelius objective functional using the velocity method International Journal of Differential Equations, 2015 (2015), Art. ID 954836, 10 pp. [PDF] · doi:10.1155/2015/954836

Talks

Upcoming Talks

• Invited TBD
  2026 Japan-Taiwan Joint Workshop on Inverse Problems and Related Topics
  Lecture Room 32, School of Science Main Building, Tsushima campus, Okayama University, Japan, November 27–29, 2026.
  Talk scheduled on November TBA, 2026.

Recent Talks

• Topological and shape optimization methods for inverse shape reconstruction
  Minisymposium on Recent Advances in Numerical Shape and Topology Optimization Methods: From Theory to Practice (organized by W. Gong, J. F. T. Rabago, and S. Zhu)
  The 19th SIAM East Asian Section Conference
  Oriental Hotel, Jeju Island, Korea, August 23–27, 2026. Talk scheduled on August 27, 2026.
• Invited Topological and shape optimization methods for inverse shape reconstruction in elliptic PDEs
  Continuum Mechanics Focusing on Singularities–Numerical Analysis & Scientific Computing 2026
  Lapu-Lapu City, Cebu, Philippines, June 20–23, 2026. Talk scheduled on June 20, 2026.
• Invited Coupling the coupled complex boundary method and ADMM for constrained shape optimization in geometric inverse problems
  The 10th Young Scholar Symposium of East Asia Section of IPIA
  National Taiwan University, Taipei, Taiwan, April 24–25, 2026. Talk scheduled on April 25, 2026.
• Invited Can we see the invisible? Mathematical methods for detecting hidden regions via shape and topological optimization
  De La Salle University, Manila City, Philippines, March 11, 2026.
• Invited Shape identification in fluid flows via shape optimization
  Workshop on Applied Mathematics and Scientific Computing
  Kanazawa, Japan, January 28, 2026.
• Invited Non-conventional shape optimization via coupled complex boundary method for shape identification problems
  Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines, December 15, 2025.
• Invited Innovative Research Approaches in Mathematics and Engineering: Trends and Opportunities
  Innovative Horizons: Advancing Research in Engineering Sciences and Mathematics
  University of Saint Louis Tuguegarao, Tuguegarao, Philippines, November 20–21, 2025. On-line talk on November 20, 2025.
• Invited An inverse shape optimization approach for localizing subdermal tumors and burns
  Faculty of Sciences and Techniques, Université Sultan Moulay Slimane, Beni Mellal, Morocco, November 4, 2025.
• Invited An inverse shape optimization approach for localizing subdermal tumors and burns
  11th International Conference on Inverse Problems, Control and Shape Optimization (PICOF'2025)
  Mehari Hammamet Hotel, Hammamet, Tunisia, October 28–31, 2025. Talk scheduled on October 30, 2025.
• Invited Numerical methods for transport coefficient recovery
  2025 International Workshop on Modeling, Analysis and Computation with Application in Economics and AI & Joint Mathematics Symposium between Shanghai University of Finance and Economics and Kanazawa University
  Shanghai University of Finance and Economics, Shanghai, China, October 25–26, 2025. Talk scheduled on October 25, 2025.
• Invited Inverse geometry via shape optimization: numerical solution and well-posedness from a moving boundary framework
  Minisymposium on Recent Advances in PDE-constrained Optimizations (organized by W. Gong, S. Zhu, and Z. Zhou)
  The Third HKSIAM Biennial Conference
  The Chinese University of Hong Kong, Hong Kong, July 7–11, 2025. Talk scheduled on July 8, 2025.
• Inverse geometric reconstruction of subdermal burn region from thermal data
  Minisymposium on Recent Advances in PDE-Constrained Optimization and Optimal Controls (organized by H. Fujiwara, W. Gong, and J. F. T. Rabago)
  The 18th SIAM East Asian Section Conference
  De La Salle University, Manila, Philippines, June 30–July 4, 2025. Talk scheduled on July 2, 2025.
• Invited Shape optimization for inverse geometry: numerical methods and well-posedness in a moving boundary setting
  Shape Seminar
  東北大学 レジリエント社会構築イノベーションセンター 306 大会議室, June 23, 2025.
• Invited Shape optimization for improved diagnosis: tumor localization and burn depth assessment
  Mathematical Society of the Philippines - CAR, Regions 1 and 2 Chapter: Mathematics Webinar Series
  online, May 24, 2025.
• Localization of tumor through a non-conventional numerical shape optimization technique
  Workshop on Modeling and Numerical Analysis of Nonlinear Phenomena 2025
  Shiinoki Cultural Complex, Kanazawa, Japan, March 16–17, 2025. Talk scheduled on March 16, 2025.
• Simultaneous reconstruction of shape and coefficients for corrosion detection via the Kohn-Vogelius approach
  第21回日本応用数理学会研究部会連合発表会
  岡山大学津島キャンパス、2025年3月5日〜3月7日. Talk scheduled on March 5, 2025.
• Invited Obstacle detection in Stokes fluid flow using a novel shape optimization approach
  Russia-Japan-India Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications"
  via MS Teams, December 11–13, 2024. Talk scheduled on December 12, 2024.
• Invited A Non-Conventional Reconstruction Approach for Parameter Identification in Inverse Optical Tomography with Single Boundary Measurement
  Inverse Days 2024
  Lapland Hotel Oulu, Oulu, Finland, December 10–13, 2024. Talk scheduled on December 11, 2024.
• Invited Applications of Moving Meshes in Numerical Shape Optimization and Moving Boundary Problems
  RIMS joint research on the Development of Numerical Analysis that Contributes to Computational Science
  RIMS共同研究・計算科学に資する数値解析学の展開
  Kyoto University, Kyoto, Japan, October 23–25, 2024. Talk scheduled on October 23, 2024.
• Invited Non-conventional shape optimization techniques for shape identification problems
  Workshop for Young Scholars: Control and Inverse Problems on Waves, Oscillations and Flows - Mathematical Analysis and Computational Methods
  若手研究集会「波動・振動・流れの制御と逆問題 -理論と数値計算-」
  Kyoto University, Kyoto, Japan, September 24–25, 2024. Talk scheduled on September 25, 2024.
• Invited Numerical shape optimization method for parameter identification problems in diffuse optical tomography with a non-convex boundary interface using a single boundary measurement
  日本応用数理学会2024年度年会
  京都大学、2024年9月14日–16日. Talk scheduled on September 14, 2024.
• A non-conventional shape optimization method for shape identification problems
  Minisymposium on Recent Advances in Numerical Shape Optimization Methods: From Theory to Practice (organized by W. Gong, S. Zhu, and J. F. T. Rabago)
  The 17th SIAM East Asian Section Conference
  University of Macau, Macao SAR, China, June 26–July 1, 2024.
• Invited Obstacle detection in Stokes fluid flow using a novel shape optimization approach
  Minisymposium on Interface motion in complex systems (organized by M. Benes and K. Sakakibara)
  ALGORITMY 2024: Central-European Conference on Scientific Computing
  High Tatra Mountains, Slovakia, March 15–20, 2024.
• Invited Non-conventional approximation procedures for parameter identification problems
  第20回日本応用数理学会研究部会連合発表会
  長岡技術科学大学、2024年3月4日〜3月6日.
• On the application of Alternating Direction of Method of Multipliers to shape identification problems
  第20回日本応用数理学会研究部会連合発表会
  長岡技術科学大学、2024年3月4日〜3月6日.
• On the coupled complex boundary method for obstacle shape recovery in Stokes fluid flow
  第25回研究集会数理設計研究部会
  香川大学町キャンパス、2023年12月19日.
• Detecting immersed obstacle in Stokes fluid using coupled complex boundary method
  2023 Joint Meeting on Applied Mathematics, Organized by the Mathematical Society of Japan
  Faculty of Advanced Science and Technology, Ryukoku University, Seta Campus, Otsu, Shiga, Japan, December 14–16, 2023.
• Invited Non-conventional shape optimization methods for solving shape inverse problems
  Minisymposium on Shape Optimization and Inverse Problems (organized by L. Afraites, A. Laurain, and J. F. T. Rabago)
  Applied Inverse Problems 2023
  University of Göttingen, Göttingen, Germany, September 4–8, 2023.
• Invited Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization setting
  Minisymposium on Interface motion and related topics (organized by M. Beneš and T. Ishiwata)
  International Congress on Industrial and Applied Mathematics 2023
  Waseda University, Tokyo, Japan, August 20–25, 2023.

Teaching

Part-Time Lecturer, Graduate Course: Applied Analysis

Kanazawa University, Kanazawa City, Japan
2026.04.06 – 2026.06.04, Q1
2025.04.07 – 2025.06.04, Q1
2024.04.08 – 2024.06.05, Q1
2023.04.06 – 2023.06.05, Q1

Adjunct Assistant Professor, Undergraduate Courses: College Algebra

Temple University, Japan Campus, Setagaya City, Japan
2024.08.26 – 2024.12.18 (2024.10.31), Fall 2024
2024.05.20 – 2024.08.07, Summer 2024
2024.01.08 – 2024.05.01, Spring 2024

Lecturer, Undergraduate Course: Pre-Calculus

University of the Philippines Baguio, Baguio City, Philippines
2015.01.22 – 2015.06.08

Instructor, Undergraduate Courses: Mathematical Biology, Elementary Analysis, and Calculus

Central Luzon State University, Science City of Muñoz, Nueva Ecija, Philippines
2013.11.12 – 2014.04.30, AY 2013-2014, 2nd Semester

Lecturer, Undergraduate Courses: Elementary Analysis, Calculus, and Pre-Calculus

Central Luzon State University, Science City of Muñoz, Nueva Ecija, Philippines
2013.06.10 – 2013.10.18, AY 2013-2014, 1st Semester
2012.11.19 – 2013.03.27, AY 2012-2013, 2nd Semester
2012.06.13 – 2012.10.26, AY 2012-2013, 1st Semester
2012.04.02 – 2012.05.11, AY 2011-2012, Summer
2011.11.08 – 2012.03.23, AY 2011-2012, 2nd Semester
2011.06.06 – 2011.10.21, AY 2011-2012, 1st Semester
2011.04.11 – 2011.05.27, AY 2010-2011, Summer

Research Meetings and Seminars

• 研究集会等の情報 (Informations on Research Meetings, etc)
• 現象数理解析研究会 (Workshop on Mathematical Analysis for Nonlinear Phenomena)
• 金沢解析セミナー (Kanazawa Analysis Seminar)
• 微分方程式とデータサイエンス研究会 (Differential Equations in Data Science)
• Shape Seminar

Events

• The 22nd Workshop on Mathematical Analysis for Nonlinear Phenomena
• International Conference: Differential Equations for Data Science 2025 (DEDS2025), Kyoto, Japan
• Workshop on Modeling and Numerical Analysis of Nonlinear Phenomena 2025 (MNANP2025), Kanazawa, Japan
• International Workshop on Computational and Mathematical Methods in Data Science 2025 (CoMaDS2025), Boracay, Aklan, Philippines
• The 18th SIAM East Asian Section Conference (EASIAM2025), Manila, Philippines
• Czech Academy of Sciences–Kanazawa University Workshop, Kanazawa, Ishikawa, Japan
• SEAMS School 2025 Baguio (Inverse Problems and Optimal Control), Baguio, Philippines
• AMSC 2026: Workshop on Applied Mathematics and Scientific Computing, Kanazawa, Ishikawa, Japan
• CoMFos-NASC 2026, Lapu-Lapu City, Cebu, Philippines
• 3rd AMSC 2026: Workshop on Applied Mathematics and Scientific Computing, Kanazawa, Ishikawa, Japan

Contacts