A full wave analysis of microstrips by the boundary element method

Classic McEliece has gathered attention as a candidate in NIST post-quantum cryptography standardization. However, it suffers from high demands on the decryption algorithm, making it unsuitable for resource-constrained devices. In this paper, we propose a novel implementation method, named giant footprint sharing, that reduces memory size during decryption in Classic McEliece. The decryption algorithm processes a large number of intermediate variables computed from a secret key in memory. The giant footprint sharing identifies the largest variable among them and allocates a memory-sharing structure to store it, thereby reducing the overall memory size regardless of the implementation platform. The giant footprint sharing can also be combined with existing acceleration techniques, such as fast Fourier transformation. We evaluate Classic McEliece with the giant footprint sharing on the Arm Cortex-M33 CPU and show that it reduces memory size by up to 46% without significant degradation in computation time compared with the existing fast-implementation by Chen et al. (at TCHES 2021). Extensive experiments with the giant footprint sharing further reveal that it maintains a constant memory size regardless of the compiler optimization, and it also achieves an optimal balance in the trade-off between memory size and computation time. The giant footprint sharing is remarkable for any scheme, that contains a large-scale matrix computation and the life cycle for each variable is limited.

The spectral-domain analysis using Chebyshev's polynomials as basis functions is used to obtain the frequency-dependent characteristics of current distributions and the effective relative permittivities of an open microstrip line. The results obtained are compared to other available results. To obtain accurately the current distributions requires a larger number of basis functions. Both longitudinal and transverse current distributions on the strip are shown for wide ranges of frequency (0 >

To analyze the light scattered from a magneto‐optical disk, a method is proposed for calculating the light scattered from a magnetic material with grooves. The model used is divided by an infinite boundary between the free space or an isotropic dielectric and an isotropic magnetic material. By using the relative permittivity of the isotropic magnetic materiel, the governing equation for the magnetic material is derived from Maxwell's equations. The three‐dimensional boundary element method is applied to this equation. The boundary element equation for free space or an isotropic dielectric material is the one in which the boundary element method is applied to a general Helmholtz equation. The one in the magnetic material is obtained by adding the volume integral in the magnetic material to the general equation. If boundary elements are large, the integral in the magnetic material near the boundary is evaluated at too small a value. The numerical results oscillate with only the foregoing method. To resolve this problem with taking practical memory size and computation time into consideration, an attenuating term is added to Green's function used in the integration in the magnetic material. With the method proposed, the optical scattering from a magnetic material can now be analyzed.

SUMMARYIn order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The obtained results are validated with literature data and then the effects of baffle flexibility on the sloshing frequencies and structural vibration frequencies are investigated. Copyright © 2011 John Wiley & Sons, Ltd.

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear elements BEM depending on the type of interpolation used at the elements. Its popularity is steadily growing because of its advantages over other numerical methods most important of which being that it only involves obtaining data at the boundary and computation of the solution in the domain is merely a case of post processing through the use of an identity. This results in the reduction of the problem dimension by unity. Although there is a reduction in dimension when we use BEM, the method usually results in full matrices which can be expensive to solve. This makes the method costly for problems that require very fine grids like those with hot spots as in the example of impressed current cathodic protection systems (ICCP). The BEM is a global method in nature in that the solution in one node depends on the solutions in all the other nodes of the grid. Hence an error in one node can pollute the solution in all the other nodes. In this thesis, we first focus our attention on defining and studying both the local and global errors for the BEM. This is not a completely new study as the literature suggests, however, our approach is different. We use the basic foundations of the the method to define the errors. Since the method is a global method, first we use the interpolation error on each element to define what we have called a sublocal error. Then using the sublocal error we have defined the local error. Understanding the local errors enabled us study the global error. Theoretical and numerical results show that these errors are second order in grid size for both the constant and linear element cases. Then, having explored errors, we study a method for adaptive grid refinement for the BEM. Rather than using a truly nonuniform grid, we present a method called local defect correction (LDC) that is based on local uniform grid refinement. This method is already developed and documented for other numerical methods such as finite difference and finite volume methods but not for BEM. In the LDC method, the discretization on a composite grid is based on a combination of standard discretizations on several uniform grids with different grid sizes that cover different parts of the domain. At least one grid, the uniform global coarse grid, should cover the entire boundary. The size of the global coarse grid is chosen in agreement with the relatively smooth behaviour of the solution outside the hot spots. Then several uniform local fine grids each of which covers only a (small) part of the boundary are used in the hot spots. The grid sizes of the local grids are chosen in agreement with the behaviour of the continuous solution in that part of the boundary. The LDC method is an iterative process whereby a basic global discretisation is improved by local discretisations defined in subdomains. The update of the coarse grid solution is achieved by adding a defect correction term to the right hand side of the coarse grid problem. At each iteration step, the process yields a discrete approximation of the continuous solution on the corresponding composite grid. We have shown how this discretisation can be achieved for the BEM. We apply the discretisation to an academic example to demonstrate its implementation and later show how to use it for an application as the ICCP system. The results show that it is a cheaper method than solving on a truly composite grid and converges in a single step.

A process of underwater explosion of a charge near a rigid wall includes three main stages: charge detonation, bubble pulsation and jet formation. A smoothed particle hydrodynamics (SPH) method has natural advantages in solving problems with large deformations and is suitable for simulation of processes of charge detonation and jet formation. On the other hand, a boundary element method (BEM) is highly efficient for modelling of the bubble pulsation process. In this paper, a hybrid algorithm, fully utilizing advantages of both SPH and BEM, was applied to simulate the entire process of free and near-field underwater explosions. First, a numerical model of the free-field underwater explosion was developed, and the entire explosion process–from the charge detonation to the jet formation–was analysed. Second, the obtained numerical results were compared with the original experimental data in order to verify the validity of the presented method. Third, a SPH model of underwater explosion for a column charge near a rigid wall was developed to simulate the detonation process. The results for propagation of a shock wave are in good accordance with the physical observations. After that, the SPH results were employed as initial conditions for the BEM to simulate the bubble pulsation. The obtained numerical results show that the bubble expanded at first and then shrunk due to a differences of pressure levels inside and outside it. Here, a good agreement between the numerical and experimental results for the shapes, the maximum radius and the movement of the bubble proved the effectiveness of the developed numerical model. Finally, the BEM results for a stage when an initial jet was formed were used as initial conditions for the SPH method to simulate the process of jet formation and its impact on the rigid wall. The numerical results agreed well with the experimental data, verifying the feasibility and suitability of the hybrid algorithm. Besides, the results show that, due to the effect of the Bjerknes force, a jet with a high speed was formed that may cause local damage to underwater structures.

The boundary node method (BNM) is a boundary-only meshfree method based on boundary integral equations (BIE). One drawback of the usual BNM, however, is that it typically requires much more computer time than the usual boundary element method (BEM). The multipole method (MM) has been demonstrated, in the context of the n body problem, and the BEM, to greatly accelerate these methods while still maintaining sufficient accuracy. The present paper explores, for the first time, a coupling of the BNM with the MM (called the BNMM) in the context of 2-D potential theory. Numerical results (for selected problems) from the BNM are compared with those from the BNMM with regard to accuracy and computational efficiency.

A new boundary element algorithm for a general solution of nonlinear space-time fractional dual-phase-lag bio-heat transfer problems during electromagnetic radiation

In positron emission tomography (PET), 3D iterative image reconstruction methods have a huge computational burden. In this paper, we developed a list-mode image reconstruction method using graphics processing units (GPUs). Efficiency of acceleration for GPU implementation largely depends on the method chosen, where a reduced number of conditional statements and a reduced memory size are required. On the other hand, accurate system models are required to improve the quality of reconstructed images. Various accurate system models for conventional CPU implementation have been proposed, but these models basically require many conditional statements and huge memory size. Therefore, we developed a new system model which matches GPU implementation better. In this model, the detector response functions, which vary depending on each line of response (LOR), are pre-computed in CPUs and modeled by sixth-order polynomial functions in order to reduce the memory size occupied in GPUs. Each element of a system matrix is obtained on-the-fly in GPUs by calculating the distance between an LOR and a voxel. Therefore the developed system model enables efficient GPU implementation of the accurate system modeling with a reduced number of conditional statements and a reduced memory size. We applied the developed method to a small OpenPET prototype, in which 4-layered depth-of-interaction (DOI) detectors were used. For image reconstruction, we used the dynamic row-action maximum likelihood algorithm (DRAMA). Compared with a conventional model for GPU implementation, in which DRFs are given as a Gaussian function of fixed width, we saw no remarkable difference for DOI data, but for non-DOI data the proposed model outperformed the conventional at the peripheral region of the field-of-view. The proposed model had almost the same calculation time as the conventional model did. For further acceleration, we tried parallel GPU implementation, and we obtained 3.8-fold acceleration by using 4 GPUs.

In this paper, we study the bilateral or unilateral contact with Coulomb friction between two elastic solids, using a domain decomposition method coupled with the boundary element method. The decomposition method we have selected is the Schur complement method, a non-overlapping technique. It enables to reduce the solution of the global problem to the solution of a problem defined only on the contact surface. Moreover, its principal advantage is that computing is done separately on each solid. We have chosen to associate it with the boundary element method. Indeed, it only requires the discretization of the boundaries of solids. This technique of coupling reduces the number of unknowns and the time of computing. We have applied it to the study of indentation of an elastic foundation by an elastic flat punch and a sphere. In this last case, our results are in conformity with the Hertz theory and the analytical solution of Spence. Moreover, we have shown the influence of friction on the size of the contact radius and on the normal pressure at centre. Copyright © 1999 John Wiley & Sons, Ltd.

Finite Element Method (FEM1) is pervasively used in most of 3D product design analysis, in which Computer Aided Design (CAD) models need to be converted in to mesh models first and then enriched with some material features and boundary conditions data, etc. The interaction between CAD models and FEM models is intensive. Boundary Element Method (BEM) has been expected to be advantageous in large-scale problems in recent years owing to its reduction of the dimensionality and its reduced complexity in mesh generation. However, the BEM application has so far been limited to relatively small problems due to the memory and computational complexity for matrix buildup are O(N2). The fast multipole BEM (FMBEM) combined with BEM and fast multipole method (FMM) can overcome the defect of the traditional BEM, and provides an effective method to solve the large-scale problem. Combining GPU parallel computing with FMBEM can further improve its efficiency significantly. Based on the three-dimensional elastic mechanics problems, the parallelisms of the multipole moment (ME), multipole moment to multipole moment (M2M) translation, multipole moment to local expansion (M2L) translation, local expansion to local expansion (L2L) translation and near-field direct calculation were analyzed respectively according to the characteristics of the FMM, and the parallel strategies under CUDA were presented in this paper. Three main major parts are included herein: (1) FMBEM theory in 3D elastostatics, (2) the parallel FMBEM algorithm using CUDA, and (3) comparison the GPU parallel FMBEM with BEM, FEM and FMBEM respectively by engineering examples. Numerical example results show the 3D elastostatics GPU FMBEM not only can speed up the boundary element calculation process, but also save memory which can be effective to solve the large-scale engineering problems.

In the boundary element method (BEM) for stress analysis, it is well known that thermal loads give rise to an additional volume integral in the primary form of the boundary integral equation (BIE). This volume integral needs to be further transformed to surface ones in order to retain the characteristic of the BEM as a boundary solution technique. In this study of the BEM for 3D thermoelasticity in general anisotropy, the fundamental solutions are expressed as Fourier series with coefficients calculated using an explicit-form Green’s function. In the exact volume-to-surface integral transformation associated with the term for the thermal effects in the BIE, a new kernel function is constructed. All formulations are implemented in an existing BEM code for 3D elastostatic analysis. Some numerical examples are presented to demonstrate the veracity of the formulations and the implementation, where the numerical results are compared with those obtained using the finite element method (FEM).

Electrostatic traveling wave (ETW) methods have shown promising performance in dust mitigation of solar panels, particle transport and separation in in situ space resource utilization, cell manipulation, and separation in biology. The ETW field distribution is required to analyze the forces applied to particles and to evaluate ETW design parameters. This study presents the numerical results of the ETW field distribution generated by a parallel electrode array using both the charge simulation method (CSM) and the boundary element method (BEM). A low accumulated error of the CSM is achieved by properly arranging the positions and numbers of contour points and fictitious charges. The BEM can avoid the inconvenience of the charge position required in the CSM. The numerical results show extremely close agreement between the CSM and BEM. For simplification, the method of images is introduced in the implementation of the CSM and BEM. Moreover, analytical formulas are obtained for the integral of Green’s function along boundary elements. For further validation, the results are cross-checked using the finite element method (FEM). It is found that discrepancies occur at the ends of the electrode array. Finally, analyses are provided of the electric field and dielectrophoretic (DEP) components. Emphasis is given to the regions close to the electrode surfaces. These results provide guidance for the fabrication of ETW systems for various applications.

PurposeThe purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.Design/methodology/approachThe key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices. Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems. The wavelet transformation part of the method can be added as a black box to existing BEM codes.FindingsNumerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented. The results show that the proposed method is efficient for large problems.Research limitations/implicationsApplication of the proposed method is restricted to problems with number of DOF equal to an integer power of 2.Originality/valueThe novel algorithm to solve transformed algebraic linear equations uses NS‐form of the modified matrix, taking the advantage of the hierarchical nature of Multi‐Resolution Analysis (MRA) to decompose a parent system into descendant systems with reduced size. These smaller systems are then solved iteratively using generalized minimal residual method.

The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.