Analysis of acoustic scattering from fluid bodies using a multipoint source model

A moment-method solution is presented for the problem of acoustic scattering from homogeneous fluid bodies. It uses fictitious isotropic point sources to simulate both the field scattered by the body and the field inside the body and, in turn, point-matches the continuity conditions for the normal component of the velocity and for the pressure across the surface of the body. The procedure is simple to execute and is general in that bodies of arbitrary smooth shape can be handled effectively. Perfectly rigid bodies are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure.     

Shape optimization of periodic structures

This paper describes a numerical approach to the optimization of effective properties of periodic perforations in an infinite body, in the frameworks of heat conduction and of linear elasticity. We implement a special finite element mesh in order to deal with the periodic nature of the problem. We compute the gradient of the functional to be minimized. We describe the process of mesh deformation and mesh regeneration. We give several numerical examples, some of them having practical relevance.     

Spherical wave scattering by slender bodies

The problem of the scattering of a spherical acoustic wave by rigid slender bodies of revolution is investigated theoretically from a formalism based on the matched asymptotic expansion method. It is an extension of a formulation that was originally derived for incident plane waves with the so-called slender-body approximation. Simple and practical formulas are obtained for the scattered pressure in the near- and far-fields: they are valid at low and medium frequencies when the reduced wavenumber Ka is less or of the order of unity. Computations of the monostatic and bistatic angular distributions for a spheroid are presented to illustrate the sensitivity of the scattered field with respect to the distance source and observation point.     

室内声场模拟中的界面声散射

室内声场模拟中引入扩散反射对提高模拟的准确性具有重要意义,但采用单值散射系数无法完整表示界面的扩散反射特性。受几何声学中扩散反射模拟方法的限制,界面有效散射系数存在不确定性。通过改变一个矩形房间中的吸声量、吸声布置方式及表面几何复杂程度等声场条件,对混响时间的模拟值与实测值进行比较,分析了由界面散射系数不确定性产生的模拟偏差与房间内声场扩散的关系。     

Shape optimization of uncemented hip prostheses

A computational model to obtain optimized geometries for the femoral component of hip prosthesis is presented. Using structural optimization techniques, the objective is to determine the shape of uncemented stems that maximize initial stability and improve performance. To accomplish this, the optimization problem is formulated by the minimization of the contact stresses and relative displacement on bone–stem interface. Design variables are geometric parameters that characterize selected cross sections. These parameters are subject to a set of linear geometric constraints in order to obtain clinically admissible geometries. Furthermore, a multiple load formulation is used to incorporate different daily life activities. Optimization results are useful to design new stems or, if integrated in an appropriate computer-aided design (CAD) system, to design custom-made hip prostheses. In the later case, the model is able to include personalized information such as patient's femur geometry and therefore personalized geometric constraints and optimization parameters.     

Shape optimization of uncemented hip prostheses

A computational model to obtain optimized geometries for the femoral component of hip prosthesis is presented. Using structural optimization techniques, the objective is to determine the shape of uncemented stems that maximize initial stability and improve performance. To accomplish this, the optimization problem is formulated by the minimization of the contact stresses and relative displacement on bone-stem interface. Design variables are geometric parameters that characterize selected cross sections. These parameters are subject to a set of linear geometric constraints in order to obtain clinically admissible geometries. Furthermore, a multiple load formulation is used to incorporate different daily life activities. Optimization results are useful to design new stems or, if integrated in an appropriate computer-aided design (CAD) system, to design custom-made hip prostheses. In the later case, the model is able to include personalized information such as patient's femur geometry and therefore personalized geometric constraints and optimization parameters.     

三维介质体的时域散射分析

用时间递推（marching—on in-time，MOT）方法求解了电磁场时域耦合积分方程，计算了均匀介质体的表面等效电流和表面等效磁流，得到时域散射远场并给出了详细推导过程。举例比较了将时域散射用Fourier变化后在频域的RCS和频域直接求得的RCS，以说明该算法的正确性。     

Shape optimization for general two-dimensional structures

Summary The growth-strain method was used for general two-dimensional shape optimization. It was verified in previous papers that the growth-strain method is very effective for shape optimization of structures with only one free surface to be deformed. But it could not provide reasonable optimized shapes for structures with two or more free surfaces such as structures with holes inside. Problems occurred, as the growth-strain method was applied to structures with two or more free surfaces. Then, an improved method was suggested. Finally, an automatic shape optimization system was built by the improved growth-strain method with commercial software using the finite element method. The effectiveness and practicability of the developed shape optimization system was verified by some examples.     

Shape analysis and injection molding optimization

Shape analysis is presented as a new approach towards optimization of polymer injection molding. Taking in consideration shape parameters such as optimal centering and skeleton transformation, the objective is to estimate the best location of the injection points to obtain lowest injection pressure and balanced filling of the mold. This paper concerns recent progress in the formulation of this problem.     

Shape optimization using adaptive shape refinement

A large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.     

Shape optimization in frictionless contact problems

A finite element approach for shape optimization in two-dimensional (2-D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary. The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B-spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented-Lagrangian techniques (to solve the contact problem) and an interior-point mathematical-programming algorithm (for shape optimization), we obtain several results reported at the end of the article.     

Fast spectral-domain method for acoustic scattering problems

This paper presents the application of the conjugate-gradient (CG) fast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFT (CG-NUFFT) method for the integral equation arising from acoustic scattering problems. In the conventional method of moments (MoM) for integral equations, the CPU and memory requirements are O(N³) and O(N²), respectively, where N is the number of unknowns in the problem. The CG-FFT method, which combines the iterative conjugate-gradient method with FFT, reduces these requirements to O(KN log₂N) and O(N), respectively, where K is the number of CG iterations. The CG-NUFFT method differs from the CG-FFT method in that it makes use of nonuniform FFT algorithms instead of FFT to allow a nonuniform discretization. Therefore, the CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method. These two methods are applied to solve for two-dimensional constant density acoustic scattering problems. Numerical. results demonstrate that they can solve much larger problems than the MoM     

Aerothermodynamic shape optimization of hypersonic blunt bodies

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier–Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.     

Shape deformations in rough-surface scattering: improved algorithms

We present new, stabilized shape-perturbation methods for calculations of scattering from rough surfaces. For practical purposes, we present new algorithms for both low- (first- and second-) and high-order implementations. The new schemes are designed with guidance from our previous results that uncovered the basic mechanism behind the instabilities that can arise in methods based on shape perturbations [D. P. Nicholls and F. Reitich, J. Opt. Soc. Am. A 21, 590 (2004)]. As was shown there, these instabilities stem from significant cancellations that are inevitably present in the recursions underlying these methods. This clear identification of the source of instabilities resulted also in a collection of guiding principles, which we now test and confirm. As predicted, improved low-order algorithms can be attained from an explicit consideration of the recurrence. At high orders, on the other hand, the complexity of the formulas precludes an explicit account of cancellations. In this case, however, the theory suggests a number of alternatives to implicitly mollify them. We show that two such alternatives, based on a change of independent variables and on Dirichlet-to-interior-derivative operators, respectively, successfully resolve the cancellations and thus allow for very-high-order calculations that can significantly expand the domain of applicability of shape-perturbation approaches.     

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush–Kuhn–Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1–4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries. Partial support for this work was provided by the US National Science Foundation under grant award CMS-0348484.     

Finite element solution for electromagnetic scattering from two-dimensional bodies

The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.     

电磁超声兰姆波换能器多目标优化设计

针对电磁超声兰姆波换能器激发的兰姆波存在多模式、频散现象和信号较弱的问题,结合铝合金板材检测背景,提出一种基于＂双交点法＂、＂零斜率准则＂和正交试验设计相结合的电磁超声兰姆波换能器多目标优化设计方法。其中,＂双交点法＂可有效削弱兰姆波多模式现象的影响,＂零斜率准则＂能够有效降低兰姆波的频散现象,而正交试验设计方法可有效提高电磁超声兰姆波信号的幅值。依据所提优化设计方法,对一个在铝板检测中常用的电磁超声兰姆波换能器的9个主要参数进行了多目标优化设计。实验表明,优化后,兰姆波信号中的多模式、频散现象得到显著抑制,而且信号幅值得到明显提升,有效改善了电磁超声兰姆波换能器的工程实用性。     

Shape optimization with topological changes and parametric control

Recent advances in shape optimization rely on free-form implicit representations, such as level sets, to support boundary deformations and topological changes. By contrast, parametric shape optimization is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. We propose a novel approach to shape optimization that combines and retains the advantages of the earlier optimization techniques. The shapes in the design space are represented implicitly as level sets of a higher-dimensional function that is constructed using B-splines (to allow free-form deformations), and parameterized primitives combined with R-functions (to support desired parametric changes). Our approach to shape design and optimization offers great flexibility because it provides explicit parametric control of geometry and topology within a large space of free-form shapes. The resulting method is also general in that it subsumes most other types of shape optimization as special cases. We describe an implementation of the proposed technique with attractive numerical properties. The explicit construction of an implicit representation supports straightforward sensitivity analysis that can be used with most gradient-based optimization methods. Furthermore, our implementation does not require any error-prone polygonization or approximation of level sets (isocurves and isosurfaces). The effectiveness of the method is demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.