A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging

During the last few years a quite large number of fluorescence molecular imaging applications have been reported in the literature, as one of the most challenging aspects in medical imaging is to “see” a tumor embedded into tissue, which is a turbid medium, by using fluorescent probes for tumor labeling. However, the forward solvers, required for the successful convergence of the inverse problem, are still lacking accuracy and time feasibility. Moreover, initialization of these solvers may be proven even more difficult than solving the inverse problem itself. This paper describes in depth a coupled radiative transfer equation and diffusion approximation model for solving the forward problem in fluorescence imaging. The theoretical confrontation of these solvers comprises the model deployment, its Galerkin finite elements approximation and the domain discretization scheme. Finally, a new optical properties mapping algorithm, based on super-ellipsoid models, is implemented, providing a fully automated simulation target construction within feasible time.     

A least square finite element formulation of the collimated irradiation in frequency domain for optical tomography applications

This paper presents an extension of the least square finite element formulation associated to the discrete ordinates method to solve collimated irradiation problems in frequency domain. The features of the method are shown with a separation of the intensity into its collimated and scattered parts for a better handling of discontinuities due to the boundary conditions of Dirichlet type used in optical tomography applications. Numerical tests are used to gauge the accuracy of the model in both isotropic and anisotropic scattering media, with and without frequency modulation. The results show that the method is accurate compared to some reference solutions.     

A strongly conservative finite element method for the coupling of Stokes and Darcy flow

We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in H^div(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders.     

小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法

有限元法可用于以声波动方程为基础通过数值计算求解室内声场,适用于分析界面阻抗非均匀分布和复杂形状房间内声场的低频特性。本文首先介绍了小阻尼界面条件下室内声场简正方式、声衰变系数、混响时间的ＦＥＭ计算方法。在此基础上导出了房间内两点之间声传输函数和声脉冲响应函数的ＦＥＭ计算模型,并以矩形房间为例详细讨论了有关细节。本文所讨论的计算模型可以映房间内不同的声源点,接收点位置上的声压频谱特性和脉冲响应的时     

Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods

The finite element and transfer matrix methods are applied in the design of a Bragg grating acousto-optic modulator. For simulation purposes, the device is taken as a single structure, composed of the silica horn and the fiber Bragg grating. The approach allows the strain field to be completely characterized along the whole structure and leads to a better understanding of the influence of the horn dimensions on the design and performance of the modulator. Results obtained using the two methods show an excellent agreement with experimental data in similar structures of the same dimensions.     

A tensor artificial viscosity using a finite element approach

We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian–Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann–Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids.     

Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid–fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone.     

稀土Tonpilz换能器的有限元设计法

当Tonpilz换能器组件迥横截面面积之间相差较大时,应力,应变会有一定的突破,边界条件将不很连续,用四端网络方法设计会带来较大的误差,本文用有限元方法,设计并研制了一稀土Tonpilz型换能器 实验测试表明,与四端网络设计法相比,有限元方法具有更好的设计精度。     

Numerical simulation of laser-generated ultrasound in non-metallic material by the finite element method

The use of a pulsed laser for the generation of the elastic waves in non-metallic materials in the thermoelastic regime is investigated by using finite element method (FEM), taking into account not only thermal diffusion and the finite spatial and temporal shape of the laser pulse, but also optical penetration and the temperature dependence of material properties. The optimum finite element model is established based on analysis of two important parameters, meshing size and time step, and the stability of solution. Temperature distributions and temperature gradient fields in non-metallic material for different time steps are obtained, this temperature field is equivalent to a bulk force source to generate ultrasonic wave. The laser-generated ultrasound waveforms at the epicenter and surface acoustic waveforms (SAWs) are obtained and the influence of optical penetration into the material on the temperature field and the ultrasound waveforms are analyzed. The numerical results indicate that the heat penetration into non-metallic material is caused mainly by the optical penetration, and the ultrasound waveforms, especially the shape of the precursor, are strongly dependent on the optical penetration depth into non-metallic material.     

Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity–pressure-Lagrange multiplier algebraic system of the discrete Navier–Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5–13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.     

小尺度阻尼边界封闭空间声传递函数的有限元素法计算

如何求解阻尼边界封闭空间中声源点到接收点的低频声传递函数已成为目前小尺度封闭空间可听化技术研究的关键技术，能处理任意形状及复杂边界条件的有限元素法可作为求解该问题的适合方法，以室内声声有源Helmholtz方程及其相应边界方程为基础，本文推导出了用于小尺度阻尼边界封闭空间声传递函数的有限元素求解方法，并编制了相应的计算机程序，在算例中，首先通过与模态叠加法计算结果进行比较，验证了该方法的正确性。最后计算了某型车体内腔中任意两点间声传递函数。     

Transmission loss predictions for dissipative silencers of arbitrary cross section in the presence of mean flow

A numerical technique is developed for the analysis of dissipative silencers of arbitrary, but axially uniform, cross section. Mean gas flow is included in a central airway that is separated from a bulk reacting porous material by a concentric perforate screen. The analysis begins by employing the finite element method to extract the eigenvalues and associated eigenvectors for a silencer of infinite length. Point collocation is then used to match the expanded acoustic pressure and velocity fields in the silencer chamber to those in the inlet and outlet pipes. Transmission loss predictions are compared with experimental measurements taken for two automotive dissipative silencers with elliptical cross sections. Good agreement between prediction and experiment is observed both without mean flow and for a mean flow Mach number of 0.15. It is demonstrated also that the technique presented offers a considerable reduction in the computational expenditure when compared to a three-dimensional finite element analysis.     

Acoustic transmission in non-uniform ducts with mean flow,part II: The finite element method

This second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non-uniform duct carrying a high speed subsonic compressible flow. A finite element scheme based on both the Galerkin method and the residual least squares method and with eight noded isoparametric elements is described. Multi-modal propagation is investigated by coupling of the solution in the duct non-uniform section to modal expansions in uniform sections. The accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified Galerkin method as introduced in Part I of this pair of papers. The results of calculations show that modal interactions, particularly in transmitted modes, become increasingly important with increasing duct flow Mach number. Power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking.     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Comparison and implementation of the various numerical methods used for calculating transmission loss in silencer systems

Issues concerning the design and use of large-scale silencers are more prevalent today then ever before. With the increased use of large industrial machinery (such as gas turbines) and the increase in public awareness and concern for noise control, the desire to be able to properly design silencers for specific applications is increasing. Even today, most silencer design is performed by simply modifying existing designs without full confidence of the new performance characteristics. Due to the size and expense of these silencers, it would be beneficial to have means to predict the insertion loss (IL) or transmission loss (TL) characteristics at the design stage. To properly accomplish this, many factors such as geometry, absorptive material properties, flow effects, break out noise, and self-generated noise must be considered. The use of the finite element method (FEM) and the boundary element method (BEM) can aid in the prediction and design. This paper examines three of the different methods used in calculation of TL values; namely the “traditional” laboratory method, the 4-pole transfer matrix method and the 3-point method. A comparison of these methods based on such criteria as accuracy, computation time, and ease of use was conducted. In addition, the idiosyncrasies and problems encountered during implementation are presented. The conclusions were that the FEM is better suited for this kind of application and that the 3-point method was the fastest method and was easier to use than the 4-pole method.     

Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media

Two finite element methods (FEMs), FEDOM1 and FEDOM2 (standing for the first and the second finite element discrete ordinates methods, respectively), are formulated and numerically tested. The reference second-order discrete equation is modified in its scattering terms and is applied to the problems of absorbing/emitting and anisotropically scattering media by using the FEM. Numerical features of the developed FEMs are compared with one of the discrete ordinates interpolation method (DOIM), which uses a finite difference scheme. Prediction results of radiative heat transfer by these two FEMs are compared with reference solutions and verified in three-dimensional enclosures containing participating media. The results of FEDOM1 and FEDOM2 agree well with exact solutions for the problem of absorbing/emitting medium with various range of optical thickness. Generally, the two FEMs show more accurate results than DOIM. And FEDOM1 shows more accurate results than FEDOM2 in most of the test problems. Both of the developed FEMs show reasonable results compared with published Monte Carlo solutions for the tested absorbing/emitting and anisotropically scattering media. Although the FEDOM2 is not as accurate as the FEDOM1, it shows its own advantages that it reduces CPU time and memory space of dependent variable to half.     

Development of a finite element model for coupled radiative and conductive heat transfer in participating media

Considering the geometrical applicability, a finite element model (FEM) for coupled radiative-conductive heat transfer has been developed which is applicable to enclosures of arbitrary geometry in present research. The present work provides a solution of coupled heat transfer in a rectangular, cylindrical or annulus enclosure with black or gray walls containing an absorbing-emitting-scattering medium. It is also applied to study the influence of conductive/radiation coefficient, albedo and wall emissivity on the temperature distribution in the medium. Compared with the results available in other references, the present FEM has no limitation with respect to geometry and can predict the coupled radiative-conductive heat transfer in participating media accurately.     

Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.