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In a previous paper (Wang, 1996) an integral equation method was given for the non-linear analysis of U-shaped bellows with uniform wall thickness. However, the wall thickness of a real U-shaped bellows varies along its profile. This paper is a continuation of the previous paper. A U-shaped bellows is still treated as a composite member consisting of circular ring shells and truncated shallow conical shells, but now the wall thickness of the truncated shallow conical shells varies with the radial co-ordinate. By using the Green function method, the non-linear integral equations of the circular ring shells and the truncated shallow conical shells are separately derived. They include four unknown parameters which are determined by junction conditions. The combined numerical procedure and corresponding program, in which the iteration method and the gradient method are respectively applied to solve the non-linear integral equations and to get approximate values of the four unknown parameters, are developed for the non-linear analysis of U-shaped bellows. Numerical results show that it is necessary to consider the wall-thickness variation; thus the decay rate of wall thickness should be taken as an important engineering parameter in the design of bellows. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper a new technique is presented for transferring the domain integrals in the boundary integral equation method into equivalent boundary integrals. The technique has certain similarities to the dual reciprocity method (DRM) in the way radial basis functions are used to approximate the body force term. However, the resulting integrals are evaluated in a much simpler way. Several examples are presented to demonstrate the validity and accuracy of the proposed paper. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper describes a substantial improvement to an existing modelling approach for two-dimensional solute transport. The flow field is represented by a series of streamtubes in which advection is simulated using a highly accurate semi-Lagrangian numerical scheme. Transverse mixing between the streamtubes is treated with a standard numerical method for diffusion. Numerical experiments demonstrate that accurate simulations of the longitudinal dispersion caused by the interaction of a simple transverse velocity profile and transverse diffusion can be obtained over a wide range of time-steps provided that the diffusion occurring during the time-step is properly accounted for. The model is ultimately limited by the relatively poor numerical treatment of transverse diffusion, but this could be remedied by employing an enhanced numerical method for this term. The paper concludes that this is an area in which future modelling efforts need to be directed. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a general rank-1 matrix formula which allows for proper rearrangement of individual terms in multiproduct forms involving vectors and matrices. A far-reaching application of the new matrix formula to eigenvalue sensitivity evaluation is presented in the paper. Such an application reduces the sensitivity expressions to elegant, very fast and recursive forms with substantial savings in computer resources. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix, which is widely used in control system applications, with respect to various parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to control and stability. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The governing equation of an elastic prismatic shaft is the two-dimensional Poisson equation defined on the cross-sectional area of the shaft. In this paper, the differential quadrature method (DQM) is employed to solve the Poisson equation on some non-rectangular domains. Singularities, which may appear in the expression of stress components or boundary conditions at a degenerated point of the grid, are removed by means of the Taylor expansion. The results of three examples are compared with the exact solutions. It is shown that accurate results can be achieved by the DQM. In addition, three geometric transformations are conducted in the third example so that the effect of mapping on the convergence and accuracy of results is investigated. It is found that rapid convergence can be fulfilled if the degenerated point of the mesh falls on a Dirichlet boundary. The approach addressed in the paper can be extended to other potential problems governed by either the Poisson equation or the Laplace equation. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Some modified AGE methods for the convection–diffusion equation are developed in this paper. Firstly, there is a treatment on the convection term in the equation which is different from that in the AGE method by Evans and Abdullah (1985). Secondly, upwind-type schemes are used for the convection dominated diffusion problems. All the modified AGE methods in the paper are unconditionally stable. The numerical example is given to show the effectiveness of the methods. The methods have the obvious property of parallelism. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recent work has shown that many ceramic fibres which are increasingly used to line industrial furnaces have highly spectral-dependent emissivities. This paper presents an extension to the standard zone method for radiative heat transfer calculations which directly models spectral variation in surface and gas properties. A short description of the zone method is given along with a summary of the weighted sum of grey gases model. This is often used as a means of representing the temperature dependence of total gas properties brought about because of the spectral non-uniformity of these properties. When surfaces as well as the gas are non-grey, a new approach is required. The method of this paper is based on dividing the spectrum into a number of bands and treating the properties as constant within each band. This method can be used directly if the boundary conditions specify all the zone temperatures. However, if some temperatures are unknown, then an iterative solution technique is required. Results of some sample calculations are presented. These illustrate the importance of directly modelling the spectral behaviour of gas and surface properties. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the problem for evaluating the eigenvalues in the buckling problem and the natural vibration problem of the bending bar is reduced to finding zeros of a function, which is called the target function T(ω) in this paper. The explicit forms of the target functions can be obtained for all possible boundary value problems. The functions depend on the numerical solution of the fundamental problems. The zeros of the target functions will be the required eigenvalues. Finally, several numerical examples are given to demonstrate the use of the suggested method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper demonstrates a simple finite element implementation of Lagrange multipliers to model the mechanical behaviour of an orthotropic composite material. The research shows the proper set of kinematic boundary conditions that must be applied in 2D plane stress elasticity to achieve the correct unit strain vectors that, upon interrogation of the associated Lagrange multipliers, give the stresses induced by these strain vectors. From these stresses the terms in the elasticity matrix can be evaluated. As well as demonstrating the correct kinematic conditions required, the paper presents the consequences of applying intuitive but incorrect conditions. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper treats a united-form solution for a point force applied at the interior of an infinite transversely isotropic solid. Several heuristic functions are adopted to obtain the expressions of the solution based on the general solution. To exclude some indeterminate attributes, the expressions are rewritten. In the final expressions, unlike previous publications where the solutions are expressed in different forms, or when some individual constants have different definitions depending on the conditions satisfied by the elastic constants, we provide united solutions which are suitable for all stable transversely isotropic materials and isotropic materials. Thus accurate numerical evaluation of the boundary element method can be performed directly without the need to resolve the singularity algebraically. Some numerical examples with BEM are also presented in this paper. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an exponentially fitted finite difference scheme of order one for the singularly peturbed Riccati equation εu′ (t) = c(t)u2(t) + d(t)u(t) + e(t), t>0, u(0) = φ with a small parameter ε multiplying the first derivative. The scheme is a modified form of Carroll's scheme (1986). The scheme is both optimal and uniform with respect to the small parameter ε, that is, the solution of the difference scheme satisfies error estimates of the form | u(ti) - ui | ≤ C min(h,ε) where C is independent of i, h and ε. Here h is the mesh size and ti is any mesh point. The scheme is explicit in nature and so no iteration is involved for the convergence of the solution. The scheme presented in this paper is new and it is different from the uniform schemes of order one available in the literature. Finally, numerical experimetns are presented. [ABSTRACT FROM AUTHOR]

The advance of powerful software for symbolic and numerical computations such as Mathematica sheds a new light on a paper by Golub and Welsch from 1969. Based on this paper the author describes a Mathematica procedure for determining the weights and abscissae of a Gauss quadrature rule with a user-defined weight function. After a brief description of the algorithm and its implementation examples demonstrate the usefulness of the procedure. The procedure is extremely useful if one has to compute many integrals with the same, possibly weakly singular, weight function. This might happen, for example, in the boundary element method. [ABSTRACT FROM AUTHOR]

In the paper the simulation of incompressible flow in 2D by the least-squares finite element method (LSFEM) in the velocity -- vorticity -- pressure version is studied. A problem with this method is that it does not conserve mass exactly, i.e. div uh ≠ 0 exactly. In the paper a modified LSFEM is developed which enforces a near zero residual of mass conservation, i.e. div u is nearly zero at every point of the discretization. This is accomplished by adding an extra restriction in the divergence free equation through the Lagrange multiplier strategy. [ABSTRACT FROM AUTHOR]

PISO (pressure-implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier-Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non-symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non-linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power-law method for modelling advection-diffusion transport. [ABSTRACT FROM AUTHOR]

In the paper a semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

An essential feature of the transient dynamic kernels for any time domain boundary integral equation is that they decay towards the static kernels for large time increments. The purpose of the paper is to show that the kernels of Mansur and Brebbia (1982), which are expressed in the form of generalized mathematical functions, do exhibit the correct decay property in contradiction to the claims of Israil and Banerjee (1990). Mansur and Brebbia express the fundamental solution wave discontinuity in terms of the generalized functions H(t) and δ(t), the Heaviside and Dirac delta functions, but do not explicitly demonstrate the required long time behaviour. In the 1990 paper the temporal discontinuity of the kernels is expressed by conventional functions in two time regimes and is shown to possess the correct long time behaviour, while it is claimed that the kernels in the 1982 paper do not. It is shown here that, assuming either constant or linear variation in time, usage of the generalized functions in the fundamental solution does yield the static fundamental solution for large time steps, as expected. [ABSTRACT FROM AUTHOR]

The geometric non-linear behaviour of thin axisymmetric circular plates on an elastic foundation is studied in the paper by using a boundary integral equation approach. A plate analogue procedure is suggested to simplify the solution. With such simplification, the foundation reaction can be arbitrary functions of plate deflection, rotation and curvatures. The boundary integral equation of thin plates and the fundamental solution of a biharmonic equation are employed for both bending and plane stress analysis. A number of numerical examples are given in the paper to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The paper presents finite difference schemes of order two for stiff initial-value problems, with a small parameter ∊ multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ∊, that is, the solution of the difference schemes satisfies error estimates of the form | u(ti)-ui| ⩽ C min(h²,∊) where C is independent of i, h and ∊. Here h is the mesh size and ti is any mesh point. The schemes presented in this paper are different from the scheme of order two available in the literature. Finally, numerical experiments are presented. [ABSTRACT FROM AUTHOR]

The stochastic boundary-element method (SBEM) is developed in this paper for 3D elastic problems and reliability analysis of structural components. The integral equations of BEM are derived partially by random variables, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results in this paper show good agreement with those obtained from Monte Carlo simulation and theoretical solutions. [ABSTRACT FROM AUTHOR]

The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples. [ABSTRACT FROM AUTHOR]

A number of improved finite-difference solutions of explicit form have been reported recently. The choice of a particular solution of these improved explicit forms is dependent on the value of the non-dimensional time step as well as whether the process involves cooling or heating. The conditions for stable operation are clarified in the paper. Two new improved solutions of implicit forms are also reported in the paper. These new solutions give better accuracy compared to the conventional Crank-Nicolson and pure implicit methods, and have unrestricted stability. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

The generalized geometric programming algorithm GOP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GOP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the `Phase I' part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist. [ABSTRACT FROM AUTHOR]

The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite-element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use. The elastic contact problems for cylinder-cylinder are solved in this paper and the results agree well with those in previous work. [ABSTRACT FROM AUTHOR]

This paper examines the suitability of three-dimensional finite elements to model accurately problems involving material incompressibility, using the displacement finite element method and exact numerical integration. The previously used method for classification of element suitability is presented and extended to the three-dimensional case. However, an alternative approach for examining suitability, quantified in terms of free degrees of freedom (equal to the degrees of freedom minus the incompressibility constraints), is introduced. This is used to examine Lagrangian cubic, serendipity cubic and tetrahedral three-dimensional elements configured in a regular cubic arrangement. The findings of this paper are substantiated by a number of three-dimensional numerical experiments and comparison with a separate two-dimensional study. All serendipity cubic elements are found to be unsuitable. The linear strain tetrahedron is on the borderline of suitability in a 6-tetrahedra-per-cube arrangement, and is thought to be only suitable if the mesh boundary nodes are not over-constrained. The same element in a 5-tetrahedra-per-cube arrangement, and higher order tetrahedra (quadratic strain etc), are suitable. The Lagrangian cube elements of higher order than the 27-node cube are suitable, but are probably not as efficient computationally as the tetrahedral elements of the same order. [ABSTRACT FROM AUTHOR]

The observation that hemodynamic forces play an important role in the pathophysiology of the cardiovascular system has led to the need for characterizing in vivo hemodynamics on a patient-specific basis. However, the introduction of computational hemodynamics in clinical research contexts is bound to the availability of integrated workflows for analyses on large populations. Since such workflows must rely on automated geometry-driven mesh generation methods, the availability of robust solvers featuring adaptive mesh refinement strategies is essential to ensure that the approach can be adopted on a large scale. In this paper, we present an open-source solver for the incompressible Navier–Stokes equations based on the libMesh finite elements library, featuring adaptive mesh refinement and parallelization. The solution scheme is a second-order velocity correction in rotational form. By presenting numerical tests on benchmark cases, we demonstrate that the coupling of this solution strategy with adaptive mesh refinement leads to a solver with good accuracy characteristics despite the relative simplicity of the scheme adopted. The availability of this solver within the Vascular Modeling Toolkit project leads to a widely available, seamless pipeline from images to simulation ready to be applied in clinical research environments. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The study of hemodynamics in arterial models constructed from patient-specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along the tubular domains. This methodology was tested with an idealized cylindrical model and three patient-specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this review paper we discuss Intelligent Systems for Medicine Laboratory's contributions to mathematical and numerical modelling of brain deformation behaviour for neurosurgical simulation and brain image registration. These processes can be reasonably described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral–tetrahedral meshes as well as meshless spatial discretization schemes. We advocate the use of total Lagrangian formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with two examples: computation of the reaction force acting on a biopsy needle, and computation of the brain shift for image registration. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the application of superplastic forming (SPF) technology to the manufacturing of maxillofacial prostheses for human implants. A combined numerical/experimental methodology is explained in detail whereby initial patient-specific data are collected in the form of computed tomography/magnetic resonance imaging scans and a final titanium alloy Ti-6A1-4V (suitably selected for bio-compatibility and osseo-integration) prosthesis is obtained for subsequent implantation into the damaged area of the patient. Various aspects ranging from the computational challenges (i.e. scanning technology, mesh generation, the finite element incremental flow formulation, pressure–time cycle) to the experimental/medical aspects (i.e. SPF laboratory conditions, patient data, SPF patient-specific process, medical feedback) will be discussed. A cranioplasty prosthesis and an orbital floor prosthesis are presented in order to show the robustness and applicability of the methodology. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A comprehensive analysis of vascular morphology and the application of generic models of vascular biomechanics to specific patients require the ability of extracting a geometrical representation of the vascular anatomy from medical images. Owing to the wide range of clinical manifestations of vascular disease and associated imaging modalities and protocols, several segmentation methods have been proposed over the last 20 years and are available in the literature. In this paper, we review the methods of segmentation of angiographic medical images and identify major advantages and disadvantages of state-of-the-art techniques. We further discuss the performance of some of the most popular intensity-based and gradient-based methods using a set of images of peripheral by-pass grafts acquired with magnetic resonance angiography (MRA). We then propose a threshold front method for the segmentation of MRA images and assess its performance using two anatomic scale replica models, reproducing a normal and a stenotic peripheral artery. The threshold front algorithm is a simple, fast and parameter-free (still adaptive) method achieving segmentation errors below pixel resolution. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the homotopy perturbation method is used to implement the nonlinear Korteweg–de Vries equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components. A suitable choice of an initial solution can lead to the needed exact solution by a few iterations. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction–diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a recent paper, the weighted essentially non-oscillatory (WENO) numerical scheme was applied to solve a multi-class Lighthill–Whitham–Richards (MCLWR) traffic flow model (J. Comput. Phys. 2003; 191:639–659). We discuss and present an enhanced WENO scheme with Lax–Friedrichs flux splitting by improving the estimation of the minimal characteristic speed of the MCLWR model, which is based on a set of inequalities of eigenvalues. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach, the matched interface and boundary (MIB) method, for the vibration analysis of rectangular plates with simply supported, clamped and free edges, and their arbitrary combinations. In previous work, the MIB method was developed for three-dimensional elliptic equations with arbitrarily complex material interfaces and geometric shapes. The present work generalizes the MIB method for eigenvalue problems in structural analysis with complex boundary conditions. The MIB method utilizes both uniform and non-uniform Cartesian grids. Fictitious values are utilized to facilitate the central finite difference schemes throughout the entire computational domain. Boundary conditions are enforced with fictitious values—a common practice used in the previous discrete singular convolution algorithm. An essential idea of the MIB method is to repeatedly use the boundary conditions to achieve arbitrarily high-order accuracy. A new feature in the proposed approach is the implementation of the cross derivatives in the free boundary conditions. The proposed method has a banded matrix. Nine different plates, particularly those with free edges and free corners, are employed to validate the proposed method. The performance of the proposed method is compared with that of other established methods. Convergence and comparison studies indicate that the proposed MIB method works very well for the vibration analysis of plates. In particular, modal bending moments and shear forces predicted by the proposed method vanish at boundaries for free edges. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Our target is to develop computational techniques for studying aerodynamic interactions between multiple objects. The computational challenge is to predict the dynamic behavior and path of the object, so that separation (the process of objects relatively falling or moving away from each other) is safe and effective. This is a very complex problem because it has an unsteady, 3D nature and requires the solution of complex equations that govern the fluid dynamics (FD) of the object and the aircraft together, with their relative positions changing in time. Large-scale 3D FD simulations require a high computational cost. Not only must one solve the time-dependent Navier–Stokes equations governing the fluid flow, but also one must handle the equations of motion of the object as well as the treatment of the moving domain usually treated as a type of pseudo-solid. These costs include mesh update methods, distortion-limiting techniques, and remeshing and projection tactics. To save computational costs, point force calculations have been performed in the past. This paper presents a hybrid between full mesh-moving simulations and the point force calculation. This mesh-moving alternative is called FOIST: fluid–object subcomputation interaction technique. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper an efficient method is developed for the formation of null bases of finite element models (FEMs) consisting of rectangular plane stress and plane strain elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-stress systems on these subgraphs. The efficiency of the present method is illustrated through three examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Currently, there is major interest within the biomedical community in developing accurate non-invasive means for analyzing bone micro-structure. This paper presents a new approach for a multi-scale finite element (FE) analysis of a trabecular structure. Two domain decomposition approaches are investigated as a basis for computational analysis at the micro-scale level, which is then applied for solving a 2D elasticity FE problem. In addition, a homogenization procedure from micro- to macro-scale level is presented. The proposed new multi-scale FE method has the potential to provide new insights into bone structure and behavior. Moreover, it is expected that the outcomes of this research will develop into a computerized virtual biopsy system. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Molecular imaging possesses the ability to characterize and measure biological processes at the cellular and molecular level in vivo. As one of the new molecular imaging modalities, bioluminescence tomography (BLT) is to reconstruct the light distribution inside a small animal from the photon flux measured on its surface. To obtain accurate and robust reconstruction, it needs a good understanding of the propagation of photons in biological tissues, which is referred to as the forward problem in BLT. Because the turbid media is high scattering and low absorption, the propagation process can be described by the steady diffusion equation. In this paper, an hp-adaptivity method for BLT forward problem is presented based on finite elements of high orders and moderate meshes by finite element method (FEM). Both numerical simulation and physical experiment are performed to evaluate the accuracy of solution and the efficiency of computation. The relevant results show that element order is more critical than mesh size to produce an accurate FEM solution efficiently. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bioluminescence tomography (BLT) is employed to reconstruct internal bioluminescent source to reveal the molecular and cellular information. However, BLT faces many challenges such as quantitative reconstruction. In this paper, a reconstruction–oriented multigrid finite element algorithm is proposed to fully reconstruct the source density. A source permissible region is utilized to raise the numerical stability. The proposed algorithm transfers diffuse equation into liner relationship between the inner source and boundary information on a mesh. A tolerant algorithm for linearly constrained optimization algorithm can solve the box-constrained quadratic optimization problem. By setting a threshold as the average reconstruction densities, we can refine every possible source element and form next mesh until the reconstructed densities are accepted. Numerical simulation of homogeneous and heterogeneous phantom demonstrates the feasibility and potential of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

While diffuse optical tomography (DOT) has been studied for years, bioluminescence tomography (BLT) is emerging as a promising optical molecular imaging tool. These two modalities have different goals. DOT is for reconstruction of optical parameters of a medium such as a breast from surface measurements induced by external sources. BLT is for reconstruction of a bioluminescent source distribution in a medium such as a mouse from surface measurements induced by internal bioluminescent sources. However, an important pre-requisite for BLT reconstruction is the knowledge on the distribution of optical parameters within the medium, which is the output of DOT. In this paper, we propose a mathematical model integrating BLT and DOT at the fundamental level; that is, performing the two types of reconstructions simultaneously instead of doing them sequentially. The model is introduced through minimizing the difference between predicted quantities and boundary measurements, as well as incorporating regularization terms. Then, we show the solution existence, introduce numerical schemes and prove convergence of the numerical solution. We also present numerical results to illustrate the utility of our approach. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Whole-body optical molecular imaging of mouse models in preclinical research is rapidly developing in recent years. In this context, it is essential and necessary to develop novel simulation methods of light propagation for optical imaging, especially when a priori knowledge, large-volume domain and a wide-range of optical properties need to be considered in the reconstruction algorithm. In this paper, we propose a 3D parallel adaptive finite element method with simplified spherical harmonics (SPN) approximation to simulate optical photon propagation in large volumes of heterogeneous tissues. The simulation speed is significantly improved by a posteriori parallel adaptive mesh refinement and dynamic mesh repartitioning. Compared with the diffusion equation and the Monte Carlo methods, the SPN method shows improved performance and the necessity of high-order approximation in heterogeneous domains. Optimal solver selection and time-costing analysis in real mouse geometry further improve the performance of the proposed algorithm and show the superiority of the proposed parallel adaptive framework for whole-body optical molecular imaging in murine models. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we extend the method of inter-modality image registration using the maximization of normalized mutual information (NMI) for the registration of [18F]-2-fluoro-deoxy-D-glucose (FDG)-positron emission tomography (PET) with T1-weighted magnetic resonance (MR) volumes. We investigate the impact on the NMI maximization with respect to using coarse-to-fine grained B-spline bases and to the number of bins required for the voxel intensity histograms of each volume. Our results demonstrate that the efficiency and accuracy of elastic, as well as rigid body, registration is improved both through the use of a reduced number of bins in the PET and MR histograms, and of a limited coarse-to-fine grain interpolation of the volume data. To determine the appropriate number of bins prior to registration, we consider the NMI between the two volumes, the mutual information content of the two volumes, as a function of the binning of each volume. Simulated data sets are used for validation and the registration improves that obtained with a standard approach based on the Statistical Parametric Mapping software. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented for the coupling of three-dimensional (3D) and one-dimensional (1D) fluid–structure-interaction models for wave propagation phenomena in flexible vessels. The method is based on the hyperbolic nature of the 1D problem. More specifically, the two Riemann invariants of the 1D problem are expressed in terms of average velocity and pressure and the value of the invariant that approaches the 3D domain provides a non-linear constraint between the two variables that is used as a boundary condition for the 3D problem. It is assumed that the distribution of the Riemann invariant is uniform in the vessel cross section. The implementation of the boundary condition in the context of a pressure-correction solution method in a finite volume mesh is described in detail. Computations of pressure pulse propagation within an elastic cylindrical vessel showed that the wave propagates smoothly from the 3D to the 1D domain. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]