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This study builds on a recent paper by Lai et al. (2018) in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal paper proposes a hybrid integral representation that combines the Sommerfeld integral and layer potential to efficiently deal with the boundaries of infinite length. In this work, we modify the integral formulation to eliminate the fictitious eigenvalues by employing the integral equation of the Burton–Miller type. We also discuss reasonable parameter settings for the hybrid integral equation to ensure efficient and accurate numerical solutions. Furthermore, we extend the modified formulation for the scattering from a cavity in a half-space whose boundary is locally perturbed. To address the cavity scattering, we introduce a virtual boundary enclosing the cavity and couple the integral equation on it with the hybrid equation. The effectiveness of the proposed method is demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. • Bound state in the continuum realized by topology optimization. • Band calculation based on the boundary element method and scattering matrix. • Novel design sensitivity derived from the adjoint variable method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 preservingthe 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. [ABSTRACT FROM AUTHOR]

Abstract: The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures. [Copyright &y& Elsevier]

Abstract: This paper presents accurate numerical solutions for nonlinear eigenvalue analysis of three-dimensional acoustic cavities by boundary element method (BEM). To solve the nonlinear eigenvalue problem (NEP) formulated by BEM, we employ a contour integral method, called block Sakurai–Sugiura (SS) method, by which the NEP is converted to a standard linear eigenvalue problem and the dimension of eigenspace is reduced. The block version adopted in present work can also extract eigenvalues whose multiplicity is larger than one, but for the complex connected region which includes a internal closed boundary, the methodology yields fictitious eigenvalues. The application of the technique is demonstrated through the eigenvalue calculation of sphere with unique homogenous boundary conditions, cube with mixed boundary conditions and a complex connected region formed by cubic boundary and spherical boundary, however, the fictitious eigenvalues can be identified by Burton–Miller's method. These numerical results are supported by appropriate convergence study and comparisons with close form. [Copyright &y& Elsevier]