This paper proposes a direct-indirect mixed Burton-Miller boundary integral equation for solving Helmholtz scattering problems with transmissive scatterers. The proposed formulation has three unknowns, one more than the number of unknowns for the ordinary formulation. However, we can construct efficient numerical solvers based on LU factorization by exploiting the sparse alignment of the boundary integral operators of the proposed formulation. Numerical examples demonstrate that the direct solver based on the proposed formulation is approximately 40% faster than the ordinary formulation when the LU-factorization-based solver is used. In addition, the proposed formulation is applied to a fast direct solver employing LU factorization in its algorithm. In the application to the fast direct solver, the proxy method with a weak admissibility low-rank approximation is developed. The speedup achieved using the proposed formulation is also shown to be effective in finding nonlinear eigenvalues, which are related to the uniqueness of the solution, in boundary value problems. Furthermore, the well-posedness of the proposed boundary integral equation is established for scatterers with boundaries of class $C^2$, using the mapping property of boundary integral operators in Hölder space.

arXiv

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Other Link： https://arxiv.org/pdf/2512.14193v1

Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.1109/globecom59602.2025.11431698

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Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.1109/ecoc66593.2025.11262935

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Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.23919/oecc/psc62146.2025.11111548

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Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.23919/isc.2025.11017731

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Authorship：Lead author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society for Industrial and Applied Mathematics  

DOI： 10.14495/jsiaml.17.61

arXiv

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.60443/jascome.24.0_73

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Authorship：Lead author,　Corresponding author   Publishing type：Research paper (scientific journal)  

This paper proposes an $O(N)$ fast direct solver for two-dimensional elastic
wave scattering problems. The proxy surface method is extended to
elastodynamics to obtain shared coefficients for low-rank approximations from
discretized integral operators. The proposed method is a variant of the
Martinsson-Rokhlin-type fast direct solver. Our variant avoids the explicit
computation of the inverse of the coefficient matrix, thereby reducing the
required number of matrix-matrix multiplications. Numerical experiments
demonstrate that the proposed solver has a complexity of $O(N)$ in the
low-frequency range and has a highly parallel computation efficiency with a
strong scaling efficiency of 70\%. Furthermore, multiple right-hand sides can
be solved efficiently; specifically, when solving problems with 180 right-hand
side vectors, the processing time per vector from the second vector onward was
approximately 28,900 times faster than that for the first vector. This is a key
advantage of fast direct methods.

DOI： 10.1016/j.enganabound.2025.106148

arXiv

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Other Link： http://arxiv.org/pdf/2411.18026v1

Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)  

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Authorship：Lead author,　Corresponding author   Language：English   Publisher：The Japan Society for Industrial and Applied Mathematics  

This paper presents a fast wavefield evaluation method for wave scattering
problems. The typical previous fast method is the fast multipole method (FMM).
The FMM, however, requires the combined use of non-fast direct evaluations near
the boundaries of scatterers. The proposed method is based on a modified
proxy-surface method accelerated interpolative decomposition. It is, therefore,
effective even if evaluation points are near the boundary and, moreover, is
free from analytical expansion of kernel functions unlike FMM. The validness
and effectiveness of the proposed method are shown by numerical examples.

DOI： 10.14495/jsiaml.16.61

CiNii Research

arXiv

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Other Link： http://arxiv.org/pdf/2403.08290v1

This paper proposes well-conditioned boundary integral equations based on the
Burton-Miller method for solving transmission problems. The Burton-Miller
method is widely accepted as a highly accurate numerical method based on the
boundary integral equation for solving exterior wave problems. While this
method can also be applied to solve the transmission problems, a
straightforward formulation may yield ill-conditioned integral equations.
Consequently, the resulting linear algebraic equations may involve a
coefficient matrix with a huge condition number, leading to poor convergence of
Krylov-based linear solvers. To address this challenge, our study enhances
Burton-Miller-type boundary integral equations tailored for transmission
problems by exploiting the Calderon formula. In cases where a single material
exists in an unbounded host medium, we demonstrate the formulation of the
boundary integral equation such that the underlying integral operator ${\cal
A}$ is spectrally well-conditioned. Specifically, ${\cal A}$ can be designed in
a simple manner that ensures ${\cal A}^2$ is bounded and has only a single
eigenvalue accumulation point. Furthermore, we extend our analysis to the
multi-material case, proving that the square of the proposed operator has only
a few eigenvalues except for a compact perturbation. Through numerical examples
of several benchmark problems, we illustrate that our formulation reduces the
iteration number required by iterative linear solvers, even in the presence of
material junction points; locations where three or more sub-domains meet on the
boundary.

arXiv

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Other Link： http://arxiv.org/pdf/2312.12787v1

Authorship：Lead author,　Corresponding author   Language：Japanese   Publisher：東京 : 日本計算数理工学会  

DOI： 10.60443/jascome.23.0_71

CiNii Research

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Other Link： https://ndlsearch.ndl.go.jp/books/R000000004-I033606274

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：Japanese   Publishing type：Doctoral thesis  

DOI： 10.14989/doctor.k22581

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)  

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Authorship：Lead author,　Corresponding author  

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Language：Japanese   Presentation type：Symposium, workshop panel (public)  

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Language：Japanese   Presentation type：Symposium, workshop panel (public)  

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Language：Japanese  

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Applicant：NTT株式会社

Application no：JP2023000334  Date applied：2023.1

Patent/Registration no：特許第7836004号  Date registered：2026.3 

J-GLOBAL

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Applicant：NTT株式会社

Application no：JP2022027943  Date applied：2022.7

Patent/Registration no：特許第7860429号  Date registered：2026.5 

J-GLOBAL

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Applicant：NTT株式会社

Application no：JP2022020587  Date applied：2022.5

Patent/Registration no：特許第7810922号  Date registered：2026.1 

J-GLOBAL

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Applicant：日本電信電話株式会社, エヌ・ティ・ティ・インフラネット株式会社

Application no：特願2021-189667  Date applied：2021.11

Announcement no：特開2023-076318  Date announced：2023.6

Patent/Registration no：特許第7693521号  Date registered：2025.6 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021030056  Date applied：2021.8

Patent/Registration no：特許第7648949号  Date registered：2025.3 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021027761  Date applied：2021.7

Patent/Registration no：特許第7575713号  Date registered：2024.10 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021027613  Date applied：2021.7

Patent/Registration no：特許第7481667号  Date registered：2024.5 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021021084  Date applied：2021.6

Patent/Registration no：特許第7568985号  Date registered：2024.10 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021021085  Date applied：2021.6

Patent/Registration no：特許第7606140号  Date registered：2024.12 

J-GLOBAL

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Applicant：日本電信電話株式会社

Application no：JP2021018144  Date applied：2021.5

Patent/Registration no：特許第7610162号  Date registered：2024.12 

J-GLOBAL

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