Details of a Researcher - Isakari, Hiroshi

Papers - Isakari, Hiroshi

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BEM-based fast frequency sweep for acoustic scattering by periodic slab

Yuta Honshuku, Hiroshi Isakari

Journal of Computational Physics (Elsevier BV) 509 113046 - 113046 2024.07

Last author, Corresponding author, Accepted, ISSN 0021-9991

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A Burton–Miller-type boundary element method based on a hybrid integral representation and its application to cavity scattering

Riku Toshimitsu, Hiroshi Isakari

Engineering Analysis with Boundary Elements (Elsevier BV) 158 303 - 312 2024.01

Last author, Corresponding author, Accepted, ISSN 0955-7997

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A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation

Yuta Honshuku, Hiroshi Isakari

Applied Mathematical Modelling (Elsevier BV) 110 819 - 840 2022.10

Last author, Corresponding author, ISSN 0307-904X

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A topology optimization of open acoustic waveguides based on a scattering matrix method

Kei Matsushima, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Wave Motion (Elsevier BV) 113 102987 - 102987 2022.08

Accepted, ISSN 0165-2125

This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai–Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.

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A robust topology optimisation for wideband structures in acoustic–elastodynamic coupled fields

Jincheng Qin, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Engineering Analysis with Boundary Elements (Elsevier BV) 140 544 - 561 2022.07

Corresponding author, Accepted, ISSN 0955-7997

On designing wave devices, perturbation in excitation frequency might give rise to serious degradation in the device performance. To address this issue, in our previous research, a robust topology optimisation (RTO) for acoustically rigid structures has been proposed. In the RTO, the angular frequency of the incident wave is assumed to be a stochastic variable subject to the normal distribution, and the uncertainty in the response is modelled using high-order Taylor's expansion. Our high-order RTO has successfully broadened the working bandwidth of acoustic devices. In this study, we extend our RTO to design viscoelastic structures involving acoustic–elastodynamic coupled waves in two dimensions. This enables us to deal with materials having more realistic acoustic properties than the rigid one. However, the computation of high-order derivatives for the coupled problem can result in low efficiency, which becomes the main difficulty in realising desirable optimisation for large scale problems. We thus propose an acceleration of our boundary element method (BEM) by employing the H-matrix method and the fast multipole method (FMM) and install the new BEM into the RTO. The proposed RTO is numerically exemplified by several acoustic designs. The results show that the proposed method can find the shape of wideband acoustic devices within a feasible computational time.

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An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics

Toru Takahashi, Tetsuro Hirai, Hiroshi Isakari, Toshiro Matsumoto

Engineering Analysis with Boundary Elements (Elsevier BV) 136 37 - 54 2022.03

Accepted, ISSN 0955-7997

This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open surface (between two layers) and (ii) a vector basis function with using the B-spline functions. Regarding (i), we considered an algorithm to generate a doubly-periodic open surface with the tensor product of the B-spline functions of any degree. Regarding (ii), we employed the vector basis function based on the B-spline functions, which was proposed by Buffa et al. (2010), and adapted it to the underlying periodic problems so that it can satisfy the quasi-periodic condition on the boundary of an open surface. The proposed IGBEM worked for solving some numerical examples satisfactorily and proved the applicability to plasmonic simulations.

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A shape optimisation with the isogeometric boundary element method and adjoint variable method for the three-dimensional Helmholtz equation

Toru Takahashi, Daisuke Sato, Hiroshi Isakari, Toshiro Matsumoto

Computer-Aided Design (Elsevier BV) 142 103126 - 103126 2022.01

Accepted, ISSN 0010-4485

This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. The boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional BEM, which is based on piecewise polynomial shape and approximate (interpolation) functions, can require many design variables because they are usually chosen as a part of the nodes of the underlying boundary element mesh. In addition, it is not easy for the conventional method to compute the gradient of the sound pressure on the surface, which is necessary to compute the shape derivative of our interest, of a given object. To overcome these issues, we employ the isogeometric boundary element method (IGBEM), which was developed in our previous work. With using the IGBEM, we can design the shape of surfaces through control points of the NURBS surfaces of the target object. We integrate the IGBEM with the nonlinear programming software through the adjoint variable method (AVM), where the resulting adjoint boundary value problem can be also solved by the IGBEM with a slight modification. The numerical verification and demonstration validate our shape optimisation framework.

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Topology optimization for incompressible viscous fluid flow using the lattice kinetic scheme

Suqiong Xie, Kentaro Yaji, Toru Takahashi, Hiroshi Isakari, Masato Yoshino, Toshiro Matsumoto

Computers & Mathematics with Applications (Elsevier BV) 97 251 - 266 2021.09

Accepted, ISSN 0898-1221

This paper presents a topology optimization method for flow channel design using the lattice kinetic scheme (LKS). LKS is a numerical scheme merging the lattice Boltzmann method with the kinetic scheme for solving the incompressible Navier-Stokes equations. In the lattice Boltzmann method, the discrete distribution functions for every grid in the analysis domain need to be stored to compute the flow field, while in the LKS, only the flow velocities and the densities are stored, and thus requiring less storage. Moreover, in the LKS, the macroscopic boundary conditions in terms of the velocity and the pressure can be imposed directly rather than considering the bounce-back boundary condition against the distribution function. In this study, the optimization is performed based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed by the adjoint variable method. Both the forward and the adjoint problems are solved using the LKS. The validity of the design sensitivity is verified by comparing it with the finite difference approximation of objective functional. Numerical examples of solving two-dimensional flow channel design problems are presented to demonstrate the proposed method.

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A robust topology optimization for enlarging working bandwidth of acoustic devices

Jincheng Qin, Hiroshi Isakari, Kouichi Taji, Toru Takahashi, Toshiro Matsumoto

International Journal for Numerical Methods in Engineering (Wiley) 122 ( 11 ) 2694 - 2711 2021.06

Corresponding author, Accepted, ISSN 0029-5981

We propose a novel robust topology optimization for designing acoustic devices that are effective for broadband sound waves. Here, we define the objective function as the weighted sum of the acoustic response to an incident wave consisting of a single frequency and its standard deviation (SD) against the frequency perturbation. By approximating the SD, under the assumption that the incident frequency follows the normal distribution, with the high-order Taylor expansion of the (conventional) objective function, we deal with significant frequency variations. To calculate such an approximation, we need to calculate the high-order frequency derivatives of the state variable. Here, we define them by integral representations, which enables us to characterize them even when the state variable is defined in an unbounded domain as is often the case with wave scattering problems. We further show that, based on this definition, the high-order derivatives can efficiently be computed by a combination of the boundary element method and automatic differentiation. We also present a derivation and calculation of the topological derivative for the newly defined objective function. We install all the proposed techniques into a topology optimization method based on the level-set method to design wideband acoustic devices. The validity and effectiveness of the proposed topology optimization are confirmed through several numerical examples.

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A topology optimisation of composite elastic metamaterial slabs based on the manipulation of far-field behaviours

Kei Matsushima, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Structural and Multidisciplinary Optimization (Springer Science and Business Media LLC) 63 ( 1 ) 231 - 243 2021.01

Accepted, ISSN 1615-147X

We propose a numerical method for a topology optimisation of composite elastic metamaterial slabs. We aim to realise some anomalous functionalities such as perfect absorption, wave-mode conversion, and negative refraction by designing the shape and topology of (visco-)elastic inclusions. Instead of manipulating effective material constants, we propose to utilise the far-field characteristics of scattered waves. This allows us to achieve novel functionalities for waves in not only low- but also high-frequency ranges. The design sensitivity corresponding to the far-field characteristics is rigorously derived using the adjoint variable method and incorporated into a level-set–based topology optimisation algorithm. The design sensitivity is computed by the boundary element method with periodic Green’s function instead of the standard finite element method to rigorously deal with the radiation of scattered waves without absorbing boundaries. We show some numerical examples to demonstrate the effectiveness of the proposed method.

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A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM

Kei MATSUSHIMA, Hiroshi ISAKARI, Toru TAKAHASHI, Toshiro MATSUMOTO

Mechanical Engineering Journal (Japan Society of Mechanical Engineers) 8 ( 1 ) 20 - 00364 2021

Accepted

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Level-set based topology optimization of transient flow using lattice Boltzmann method considering an oscillating flow condition

Truong Nguyen, Hiroshi Isakari, Toru Takahashi, Kentaro Yaji, Masato Yoshino, Toshiro Matsumoto

Computers & Mathematics with Applications (Elsevier BV) 80 ( 1 ) 82 - 108 2020.07

Accepted, ISSN 0898-1221

Topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering. Specifically, the development of energy dissipation devices with vibration control remains a key consideration. The aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice Boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real-world engineering designs. Although several studies have examined topology optimization to minimize dissipated kinetic energy, this study introduces an objective function for maximizing the dissipated kinetic energy in time-varying fluid flows via velocity gradients.

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A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices

Toru Takahashi, Tatsuro Yamamoto, Yuta Shimba, Hiroshi Isakari, Toshiro Matsumoto

Engineering with Computers (Springer London) 35 ( 2 ) 1 - 27 2018.04

Accepted, ISSN 1435-5663

We propose a gradient-based optimisation framework to design the shape of the interfaces in periodic layered structures, which can model photovoltaic devices, optical gratings, etc., according to a desired electromagnetic property. To this end, we first develop an isogeometric boundary element method (IGBEM) to analyse singly periodic boundary value problems for 2D Helmholtz equation in layered media. By nature, the IGBEM is not only numerically accurate but also suitable for the shape optimisation in comparison with the conventional boundary- and domain-type solvers. Next, we derive the shape derivative (or shape sensitivity) of the objective function in terms of the magnetic field strength or energy absorption rate on the basis of the adjoint variable method. The shape derivative can be computed by solving the primal and adjoint problems with the IGBEM. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a general-purpose software for the latter problems. After verifying our optimisation framework rigorously by comparing with the exact solutions, we demonstrate a shape optimisation of the silicon-metal interface in a model of thin-silicon photovoltaic devices: it is crucial to determine the interface so that the energy of the incident light can be confined in the silicon layer as much as possible when the thickness of the layer is unconventionally small
one micrometre in our model. The optimal shape achieved 8.6 times higher absorption rate than the reference (flat) shape. This simulation shows that the proposed framework is capable of making a fundamental contribution to analysing and designing photovoltaic devices as well as photonic and plasmonic devices that consist of singly periodic layers.

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A level-set-based topology optimisation for acoustic-elastic coupled problems with a fast BEM-FEM solver

Hiroshi Isakari, Toyohiro Kondo, Toru Takahashi, Toshiro Matsumoto

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (ELSEVIER SCIENCE SA) 315 501 - 521 2017.03

Lead author, Corresponding author, Accepted, ISSN 0045-7825

This paper presents a structural optimisation method in three-dimensional acoustic elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic elastic coupled problems. In this paper, the acoustic elastic coupled problems are solved by a BEM-FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method. (C) 2016 Elsevier B.V. All rights reserved.

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A level-set-based topology optimisation of carpet cloaking devices with the boundary element method

NAKAMOTO Kenta, ISAKARI Hiroshi, TAKAHASHI Toru, MATSUMOTO Toshiro

Mechanical Engineering Journal (The Japan Society of Mechanical Engineers) 4 ( 1 ) 16 - 00268-16-00268 2017

Corresponding author, Accepted

<p>We investigate a topology optimisation based on the level set method for a design problem of carpet cloaking devices. In topology optimisation of carpet cloaking devices, we need to calculate the electromagnetic response in a semi-infinite domain. We use the boundary element method (BEM) for the electromagnetic analysis since the BEM is more suitable to topology optimisation in wave field than the finite element method; the infinite domain can be evaluated exactly and mesh generation is required only on a boundary with the BEM. Along with the detailed formulation of the BEM-based topology optimisation, we present some numerical examples of design for carpet cloaks. We have confirmed that the designed carpet cloaking devices effectively work for the cases where permittivity, wavelength and angle of incidence are fixed. In addition, we have confirmed that cloaking devices for perturbed permittivity and wavelength can be obtained by redefining the objective function with the KS function.</p>

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Periodic band structure calculation by the Sakurai-Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation

Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS (ELSEVIER SCI LTD) 68 42 - 53 2016.07

Accepted, ISSN 0955-7997

In this paper, we present a numerical method for periodic band structure calculation, which is associated with eigenvalue problems for periodic problems, using the boundary element method (BEM). In the BEM, the eigenvalue problems are converted into non-linear eigenvalue problems, which are not tractable with conventional eigensolvers. In the present study, to solve non-linear eigenvalue problems, the block Sakurai-Sugiura (SS) method, which can convert non-linear eigenvalue problems into generalised eigenvalue problems, is utilised. A fast direct solver for the BEM with a fast multipole representation is employed in the algorithm of the block SS method since algebraic equations need to be solved for multiple right-hand sides in the block SS method. We conduct several numerical experiments related to phononic structures to confirm the validity and efficiency of the proposed method. We confirm that the proposed method can calculate the band structure of the phononic structures, and the computational time with the proposed method is less than that with a conventional FEM-based eigensolvers with triangular linear elements even for relatively small problems. (C) 2016 Elsevier Ltd. All rights reserved.

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An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions

Toru Takahashi, Yuta Shimba, Hiroshi Isakari, Toshiro Matsumoto

COMPUTER PHYSICS COMMUNICATIONS (ELSEVIER SCIENCE BV) 202 151 - 164 2016.05

Accepted, ISSN 0010-4655

We propose an efficient scheme to perform the multipole-to-local (M2L) translation in the three-dimensional low-frequency fast multipole method (LFFMM). Our strategy is to combine a group of matrix vector products associated with M2L translation into a matrix matrix product in order to diminish the memory traffic. For this purpose, we first developed a grouping method (termed as internal blocking) based on the congruent transformations (rotational and reflectional symmetries) of M2L-translators for each target box in the FMM hierarchy (adaptive octree). Next, we considered another method of grouping (termed as external blocking) that was able to handle M2L translations for multiple target boxes collectively by using the translational invariance of the M2L translation. By combining these internal and external blockings, the M2L translation can be performed efficiently whilst preserving the numerical accuracy exactly. We assessed the proposed blocking scheme numerically and applied it to the boundary integral equation method to solve electromagnetic scattering problems for perfectly electrical conductor. From the numerical results, it was found that the proposed M2L scheme achieved a few times speedup compared to the non-blocking scheme. (C) 2016 Elsevier B.V. All rights reserved.

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A multi-objective topology optimisation for 2D electro-magnetic wave problems with the level set method and BEM

Hiroshi Isakari, Kenta Nakamoto, Tatsuya Kitabayashi, Toru Takahashi, Toshiro Matsumoto

European Journal of Computational Mechanics (Taylor and Francis Ltd.) 25 ( 1-2 ) 165 - 193 2016.03

Accepted, ISSN 1958-5829

We have been investigating applications of a level set-based topology optimisation for wave devices with the boundary element method. For two-dimensional electro-magnetic wave problems, we have, so far, proposed a topology optimisation which can find a configuration of dielectric materials to locally minimise an objective functional such as the intensity of transverse electric (TE) or transverse magnetic (TM) polarised wave with a specific frequency. As an extension of our methodology, this paper presents a multi-objective topology optimisation, which can deal with some objective functionals simultaneously. The present method, for instance, can find a material distribution which can locally minimise the intensity of both TM and TE waves with multiple frequencies. The basic idea of the proposed method is to use the weighted sum or the Kreisselmeier–Steinhause function of the original objective functionals as a new objective functional. We present a derivation of the topological derivative for the new objective functional, and a detailed algorithm of the optimisation process with the derived topological derivative. We also present some numerical examples to illustrate the validity and efficiency of the proposed method.

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Level set-based topology optimization for 2D heat conduction problems using BEM with objective function defined on design-dependent boundary with heat transfer boundary condition

Guoxian Jing, Hiroshi Isakari, Toshiro Matsumoto, Takayuki Yamada, Toru Takahashi

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS (ELSEVIER SCI LTD) 61 61 - 70 2015.12

Accepted, ISSN 0955-7997

This paper proposes an optimum design method for two-dimensional heat conduction problem with heat transfer boundary condition based on the boundary element method (BEM) and the topology optimization method. The level set method is used to represent the structural boundaries and the boundary mesh is generated based on iso-surface of the level set function. A major novel aspect of this paper is that the governing equation is solved without ersatz material approach and approximated heat convection boundary condition by using the mesh generation. Additionally, the objective functional is defined also on the design boundaries. First, the topology optimization method and the level set method are briefly discussed. Using the level set based boundary expression, the topology optimization problem for the heat transfer problem with heat transfer boundary condition is formulated. Next, the topological derivative of the objective functional is derived. Finally, several numerical examples are provided to confirm the validity of the derived topological derivative and the proposed optimum design method. (C) 2015 Elsevier Ltd. All rights reserved.

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A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

Hiroshi Isakari, Kohei Kuriyama, Shinya Harada, Takayuki Yamada, Toru Takahashi, Toshiro Matsumoto

Mechanical Engineering Journal 1 ( 4 ) CM0039 2014.08

Accepted

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