Application of high-order boundary elements to the electrocardiographic inverse problem

Eight-noded quadrilateral boundary elements are applied to the electrocardiographic inverse problem as an example for high-order boundary elements. It is shown that the choice of the shape functions used for approximation of the potentials has a remarkable influence on the solution obtained if the number of electrodes is smaller than the number of primary source points (under-determined equation system). Three different formulations are investigated considering a concentric spheres problem where an analytic solution is available: (a) the isoparametric formulation; (b) the quasi-first-order formulation; and (c) the pseudo-subparametric formulation as a new method. In a second step the pseudo-subparametric formulation (which provided the best results in the test problem) is applied to real word data. The transmembrane potential pattern of a 40 years old female suffering from severe heart failure and ventricular tachycardia after large anterior wall myocardial infarction is reconstructed for one time instant. Furthermore, an algorithm for the calculation of the transfer matrix is presented which avoids restrictions to the boundary element mesh caused by the placement of the electrodes.     

用边界粒子法求解柯西反问题的数值计算软件包

为推动无网格方法在反问题中的应用及相关计算软件的发展,介绍基于MATLAB开发的用边界粒子法(Boundary Particle Method,BPM)数值模拟柯西反问题的计算软件包;描述数值算法的理论基础,并结合标准算例介绍软件包的基本功能和使用方法.该软件包可求解含不同形式源项(多项式函数、三角函数、指数函数及其耦合函数等)的椭圆型偏微分方程,并且可用于处理任意几何区域问题.本软件包具有简单易用的图形用户界面,在数值模拟柯西反问题时仅需边界测量数据,且效率高、精度高.     

Analog methods for computation of the generalized inverse

In this paper some properties of the generalized matrix inverse are discussed leading up to two analog techniques for its computation. Analog procedures are given for the computation of the unique vectorxof least Euclidean norm that minimizes the Euclidean norm of the error vectorAx - b.     

Flow field computation for the high voltage gas blast circuit breaker with the moving boundary

We studied the gas dynamics for the ideal gas in the simplified high voltage (HV) gas blast circuit breaker with the moving boundary. The piston and the electric contact are moving. Since the boundary is moving, it is difficult for the ordinary finite difference (FD) method or the finite element (FE) method to compute the solution. For the purpose of numerical simplicity and efficiency, we introduced an upwind meshfree scheme which is an excellent scheme for the time varying domain. Despite the low coding and computational cost, the numerical simulation is successfully conducted. Our method is even more efficient when considering a three-dimensional computation with a moving boundary.     

Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary

Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.     

Single- and multi-objective shape design of Y-noise barriers using evolutionary computation and boundary elements

The optimum shape design of Y-noise barriers is carried out using single and multi-objective evolutionary algorithms and the Boundary Element Method (BEM). Reduction of noise impact efficiency (using the insertion loss-IL-magnitude) and cost of the barrier (using its total length magnitude) are considered. A two-dimensional problem of sound propagation in the frequency domain is handled, defined by a fixed position emitting source, which pulses in a frequency range, and receptor. A noise barrier (limiting its maximum effective height) is situated between both. Its shape is modified to minimize the receptor measured sound level, which is calculated using BEM. Results of an inverse problem using the IL barrier curve as reference are successfully performed to validate the methodology. The proposed methodology is then used to obtain Y-barriers with 15% and 30% improved IL spectrum. Finally, six non-dominated solutions of the multi-objective optimum design problem are presented in detail.     

Solid-to-shell transition elements for the computation of interlaminar stresses

This paper presents an accurate and practical technique for coupling shell element models to three-dimensional continuum finite element models. The compatibility between these two types of formulations is enforced by degenerating a continuum element through kinematic constraints compatible with shell deformations. Two formulations of two-dimensional/three-dimensional transition elements are presented. The first and simplest formulation is based on the Mindlin-Reissner plate assumptions, and is found to perform well in a variety of problems involving the analysis of geometrically linear/non-linear laminated structures. The second formulation is based on a higher-order shell theory that allows stretching in the through-the-thickness direction. This additional freedom virtually eliminates the interlaminar normal stress boundary layer that can form in lower-order transition elements. Finally, the coupling of two-dimensional to three-dimensional subdomains is enriched with the use of an interface element, which can be used in conjunction with either transition formulation. The interface element improves the efficiency of the solid-to-shell transition modeling scheme by allowing the independent selection of optimal mesh sizes in the shell and the three-dimensional regions of the model.     

On the computation of the generalized Vandermonde matrix inverse

Starting from the procedure described in [1], a modified method for finding the inverse of the Vandermonde matrix is presented.     

Moment computation for objects with spline curve boundary

A new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary. The explicit formulae are obtained for area and low order moment calculation. The complexity of calculation depends on the moment order, spline degree, and the number of control points used in spline representation. The formulae proposed use the advantage that the sequence of spline control points is cyclic. It allowed us to reduce substantially the number of summands in them. The formulae might be useful in different applications where it is necessary to perform measurements for shapes with a smooth boundary.     

Procedure for manipulator inverse kinematics computation and proper pseudoinverse perturbation

In this article, an efficient procedure for the proper pseudoinverse perturbation and the numerical inverse kinematics computation of robot manipulators is presented. The approach is based on solving a linear system of equations and using an original scheme for the appropriate perturbation of the pseudoinverse matrix in the next iteration. The resultant algorithm is tested on the simulation of an industrial robot manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.     

On the computation of a matrix inverse square root

The inverse square root of a matrix plays a role in the computation of an optimal symmetric orthogonalization of a set of vectors. We suggest two iterative techniques to compute an inverse square root of a given matrix. The two schemes are analyzed and their numerical stability properties are investigated.     

Complex boundary elements for contaminant transport

Recent numerical advances in the Complex Variable Boundary Element Method (CVBEM) provide easier-to-use analysis procedures in the study of advection-dominated contaminant transport of conservative specie migration in a steady groundwater flow field. In this paper, the CVBEM is applied to groundwater advection contaminant transport problems, and the CVBEM numerical error is evaluated by use of the approximate boundary graphical technique. Besides providing actual solutions to many groundwater flow and advective contaminant transport problems, the CVBEM can be used to develop analytic test cases to be used in numerically calibrating other groundwater and contaminant transport numerical models for other classes of problems. In this paper, the CVBEM model is developed by use of a coupled L²/Collocation fit to prescribed boundary conditions.     

A mixed finite element method for boundary flux computation

Most finite element schemes for thermal problems estimate boundary heat flux directly from the derivative of the finite element solution. The boundary flux calculated by this approach is typically inaccurate and does not guarantee a global heat balance.In this paper we present a mixed finite element method for calculating the boundary flux and show the superiority of this method through numerical examples of both diffusion and advection-diffusion problems.     

A fast procedure for manipulator inverse kinematics computation and singularities prevention

In this article, a fast procedure for numerical manipulator inverse kinematics computation and singularities prevention is presented. The approach is based upon solving a linear system and automatically calculating some parameters. These parameters are properly used in either one of two original schemes that are also proposed to induce robustness to the pseudoinverse. Furthermore, here it is also shown how to properly implement one of these schemes in conjunction with a recently developed approach for the singularities prevention of redundant manipulators. The resultant algorithms are tested on the simulation of a planar redundant manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.     

Using graphics processors to accelerate the computation of the matrix inverse

We study the use of massively parallel architectures for computing a matrix inverse. Two different algorithms are reviewed, the traditional approach based on Gaussian elimination and the Gauss–Jordan elimination alternative, and several high performance implementations are presented and evaluated. The target architecture is a current general-purpose multicore processor (CPU) connected to a graphics processor (GPU). Numerical experiments show the efficiency attained by the proposed implementations and how the computation of large-scale inverses, which only a few years ago would have required a distributed-memory cluster, take only a few minutes on a hybrid architecture formed by a multicore CPU and a GPU.     

Reordering computation sequences for memory-efficient binary field multiplication

Finite field multiplication is a crucial building block for cryptography, especially the elliptic curve public key cryptosystem. Recently, various algorithms for efficient finite field multiplication over devices whose resources are extremely constrained have been proposed. However, most of these proposals only take speed optimization into account, but they do not pay much attention to optimization of memory usage. In this paper, we propose a multiplication algorithm on $F_{2^{m}}$ , which minimizes the RAM requirement by rescheduling operation sequences. According to our experimental results on the ATmega128L microprocessor, the proposed algorithm reduces the amount of required RAM by up to 50 % while maintaining the speed at the same level. We also verify the feasibility of our algorithm by applying it to the elliptic curve cryptosystem.     

A posteriori error estimate for the symmetric coupling of finite elements and boundary elements

In this note we study a posteriori error estimates for a model problem in the symmetric coupling of boundary element and finite elements methods. Emphasis is on the use of the Poincaré-Steklov operator and its discretization which are analyzed in general for both a priori and a posteriori error estimates. Combining arguments from [6] and [9, 10] we refine the a posteriori error estimate obtained in [9, 10]. For quasi-uniform meshes on the boundary, we prove some inequality of a reverse type using techniques from [5] and [36]. This indicates efficiency of the new estimate as illustrated in a numerical example.