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

Research Project

Project/Area Number 23K13012
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionKanazawa University

Principal Investigator

Rabago JuliusFergy  金沢大学, 数物科学系, 博士研究員 (10897995)

Project Period (FY) 2023-04-01 – 2027-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2026: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2025: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsinverse geometry problem / ADMM / shape optimization / shape identification / Shape inverse problems
Outline of Research at the Start

This research aims to effectively and accurately solve time-dependent inverse geometry problems with complex geometries and under noisy data by developing non-conventional solution methods. The analysis of the problems at long time horizons and rigorous mesh sensitivity analysis are carried out to support the method's development. A wide range of analytical methods such as numerical analyses and tools from optimal control theory are required. Important applications from small to large scale problems such as identification of tumor shapes and exploration of geological resources are expected.

Outline of Annual Research Achievements

During the last fiscal year, as part of my research plan, I had three papers published, one accepted paper, and two submitted manuscripts, all in highly respected peer-reviewed journals. The results were presented in three international conferences and three local scientific meetings.

The first published paper addresses an inverse problem within the context of the stationary advection-diffusion problem. The second published paper examines a novel and stable shape optimization method for free surface problems with Stokes flow, achieved through the coupling of boundary data as a complex Robin-type boundary condition. The accepted paper establishes results on existence, stability analysis, and inversion via multiple measurements for boundary shape reconstruction, providing more accurate reconstructions of the unknown shapes. The two submitted papers explore the application of the new coupled complex boundary method to obstacle detection in Stokes fluid flow and present the development of a novel robust alternating direction method of multipliers for solving geometric inverse problems in a shape optimization setting. These papers align closely with the objectives outlined in Project (A) of the proposal.

The other published paper introduces a comoving mesh method for multi-dimensional moving boundary problems which plays a crucial role in developing shape optimization methods for time-dependent problems. The results of this study are directly relevant to the theme of the proposed research.

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

Several objectives specified in the proposal have been accomplished through the papers that have been published and submitted. The findings within these papers suggest that dealing with the more demanding elements of the proposal, which encompass time-dependent cases of the model equations, could present more difficulties. Nonetheless, they also underscore the existence of several captivating nuanced issues that demand comprehension before addressing the more challenging objectives. At present, my attention is directed towards identifying and resolving these finer issues related to gradient flows within stationary contexts.

Strategy for Future Research Activity

Instead of directly addressing the more challenging aspects of the proposal, my current focus lies in delving into the intriguing questions surrounding gradient flows, which originated from the initial phase of the proposal. These inquiries have already been addressed to some extent within the context of stationary problems. I anticipate that the findings of these investigations will offer valuable insights for navigating the ambitious components of the proposal in subsequent stages.

Report

(1 results)
  • 2023 Research-status Report
  • Research Products

    (15 results)

All 2024 2023 Other

All Int'l Joint Research (2 results) Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results) Presentation (8 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results) Remarks (1 results)

  • [Int'l Joint Research] Sultan Moulay Slimane University(モロッコ)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Ibn Zohr University(モロッコ)

    • Related Report
      2023 Research-status Report
  • [Journal Article] Comoving mesh method for multi-dimensional moving boundary problems: Mean-curvature flow and Stefan problems2024

    • Author(s)
      Sunayama Yosuke、Rabago Julius Fergy Tiongson、Kimura Masato
    • Journal Title

      Mathematics and Computers in Simulation

      Volume: 221 Pages: 589-605

    • DOI

      10.1016/j.matcom.2024.03.020

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Shape reconstruction for advection-diffusion problems by shape optimization techniques: The case of constant velocity2024

    • Author(s)
      Cherrat Elmehdi、Afraites Lekbir、Rabago Julius Fergy Tiongson
    • Journal Title

      Discrete and Continuous Dynamical Systems - S

      Volume: 0 Issue: 1 Pages: 0-0

    • DOI

      10.3934/dcdss.2023186

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Boundary shape reconstruction with Robin condition: existence result, stability analysis, and inversion via multiple measurements2024

    • Author(s)
      Afraites Lekbir、Rabago Julius Fergy Tiongson
    • Journal Title

      Computational and Applied Mathematics

      Volume: 0 Issue: 5 Pages: 0-0

    • DOI

      10.1007/s40314-024-02741-3

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting2023

    • Author(s)
      Rabago Julius Fergy Tiongson、Notsu Hirofumi
    • Journal Title

      Applied Mathematics & Optimization

      Volume: 89 Issue: 1 Pages: 2-2

    • DOI

      10.1007/s00245-023-10065-7

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Presentation] Obstacle detection in Stokes fluid flow using a novel shape optimization approach2024

    • Author(s)
      Rabago Julius Fergy Tiongson、Afraites Lekbir、 Notsu Hirofumi
    • Organizer
      Mini-symposium on Interface Motion in Complex Systems, ALGORITMY 2024: Central-European Conference on Scientific Computing
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] Non-conventional approximation procedures for parameter identification problems2024

    • Author(s)
      Rabago Julius Fergy Tiongson、 Notsu Hirofumi
    • Organizer
      第20回日本応用数理学会研究部会連合発表会
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] On the application of alternating direction of method of multipliers to shape identification problems2024

    • Author(s)
      Rabago Julius Fergy Tiongson、Hadri Aissam、Afraites Lekbir
    • Organizer
      第20回日本応用数理学会研究部会連合発表会
    • Related Report
      2023 Research-status Report
  • [Presentation] On the coupled complex boundary method for obstacle shape recovery in Stokes fluid flow2024

    • Author(s)
      Rabago Julius Fergy Tiongson、Afraites Lekbir、 Notsu Hirofumi
    • Organizer
      第25回研究集会数理設計研究部会
    • Related Report
      2023 Research-status Report
  • [Presentation] Detecting immersed obstacle in Stokes fluid using coupled complex boundary method2023

    • Author(s)
      Rabago Julius Fergy Tiongson、Afraites Lekbir、 Notsu Hirofumi
    • Organizer
      2023年度応用数学合同研究集会
    • Related Report
      2023 Research-status Report
  • [Presentation] Non-conventional shape optimization methods for solving shape inverse problems2023

    • Author(s)
      Rabago Julius Fergy Tiongson、Hadri Aissam、Afraites Lekbir
    • Organizer
      Mini-symposium on Shape Optimization and Inverse Problems, 11th Applied Inverse Problems 2023
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the new coupled complex boundary method for shape inverse problem with the Robin homogeneous condition2023

    • Author(s)
      Afraites Lekbir、Rabago Julius Fergy Tiongson
    • Organizer
      Mini-symposium on Shape Optimization and Inverse Problems, 11th Applied Inverse Problems 2023
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization setting2023

    • Author(s)
      Rabago Julius Fergy Tiongson、 Notsu Hirofumi
    • Organizer
      Mini-symposium on Interface Motion and Related Topics, 10th International Congress on Industrial and Applied Mathematics
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Julius Fergy Tiongson Rabago

    • URL

      https://jftrabago.github.io

    • Related Report
      2023 Research-status Report

URL: 

Published: 2023-04-13   Modified: 2024-12-25  

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