ICCG Method Research Articles

Computation of electrostatic lenses and multipoles by the first order finite element method

The use of the first order finite element method for the computation of electrostatic rotationally symmetric electron lenses and electrostatic multipole elements is described. Attention is paid to the correct evaluation of the coefficients of FEM equations. Specific features in the program implementation include the use of thin electrodes, the use of dense fine mesh with smoothly varying step size, and the solution of the resulting set of linear equations with a fast and efficient ICCG method. The program is equipped with a suitable user interface allowing data input and modification graphically or by editing in clearly arranged menus, automeshing procedure for the generation of the fine mesh, and allowing display and plotter output of computed results. In a related program for electrostatic multipoles higher order harmonic components can be calculated. The use and the accuracy of the programs is illustrated by an example of the computation of a two-tube electrostatic lens, and by the evaluation of the axial multipole function for higher multipoles.

Massively parallel computation using a splitting-up operator method for three-dimensional device simulation

This paper presents a new parallel algorithm and performance results of iterative solution methods for three-dimensional MOSFET simulation with Gummel's method. A splitting-up operator method is proposed for incomplete factorization of sparse matrices arising from semiconductor device equations, suitable for parallel computations. This method is combined with the conjugate gradients and BiCGSTAB procedure to obtain a new parallel version of the iterative solution methods. Natural parallelism is realized by developing the solution method according to the natural ordering. In large-scale simulations of greater than 100000 grid nodes, the high parallel efficiency level over 90% can be achieved using a new-type massively parallel computer: ADENART with up to 256 processors. The real performance of the solution methods is superior to those calculated by the vectorized version of the ICCG and ILUBiCGSTAB methods using a vector-type supercomputer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

3-D plasma armature railgun simulations

A three-dimensional Navier-Stokes code has been extended to provide a simulation for the railgun plasma armature. This code was previously used with an approximate electromagnetic model to provide a two-dimensional simulation of a railgun plasma armature flow in the plane containing the insulators. A new three-dimensional electromagnetic solver has been incorporated into the code to permit full 3-D nonsteady MHD simulations of the plasma armature flow in a railgun. The finite-difference equations for magnetic vector potential and electric potential are solved using the ICCG method. The new electromagnetic solver was validated using 3-D solutions obtained from the finite element electromagnetic code MEGA. A full bore, 3-D simulation of a plasma armature reveals flow patterns significantly different than those of rail or insulator plane 2-D simulations. In particular, the maximum J/spl times/B force occurs off-axis and results in a plasma flow away from the projectile along the axis of symmetry. A zone of high shear flow forms near the rail surfaces which increases the viscous losses. Zones of low current, nearly stagnant flow form near the base of the projectile, consistent with experimental observations of a buffer between the armature and the projectile. >

辺要素法三次元磁場解析における電流連続入力方法

3D magnetic field calculation using edge elements is very useful for designing magnetic devices, because of its speed and accuracy. However, the linear equations obtained in the edge element method have no solutions unless an exciting current density is input so as to satisfy the condition of current continuity. This makes it difficult to apply the edge element method to magnetic field calculation when the shape of a coil and its divided meshes are complicated. The present paper describes a practical method that can overcome this problem and includes an additional means of solving problems related to the convergence of calculation. This method ensures that the iterative calculation by the ICCG method converges. The flux density distribution of a flat transformer is calculated by using this method, and the results show that the calculated values agree with the measured values within a range of 3.3%.

Further developments of iccg and miccg

Using the order matrix of the LU factors of A obtained from the 5-point discretization of the model self-adjoint elliptic problem, a P-order fill-in is suggested to give the incomplete LU decompositions, where P = 0,1,2,.... This strategy produces a series of incomplete LU factors which has the identical sparse structure with the series of ICCG(s,t) preconditioner for (s,t) = (1,1), (1,2), (1,3), (2,4), (3,5),.... The order matrices of the corresponding error matrices are given and some of their properties are discussed. According to the modified P-order truncated elimination, a simplified factorisation procedure is presented for the P-order ICCG method to reduce the factorisation costs. A similar procedure is also presented for the P-order MICCG method. Numerical results show that the simplification does not impair the convergence rate. It is demonstrated that sometimes a stagnation may happen in the numbers of MICCG iterations. This is caused by the parameter ξ used in the method. A rational manner to s...

Two-dimension numerical simulation of submicron-scale GaAs mesfet

This paper deals with 2-D simulation of GaAs MESFET, which includes velocity overshoot effects by using energy transport model suitable for submicron devices. Computation time is greatly reduced by simplifying the model and using fast convergence algorithms, e.g. Gummel interaction and ICCG method. The program shows good stability and convergence. Several types of GaAs MESFET structures, e.g., epitaxial ion-implanted and buriedP-layer, have been simulated. The results show that buriedP-layer can decrease carrier’s injections into substrate and improve device performance. The results are also used to study carefully the velocity overshoot effects. By comparison of results of energy transport model and drift-diffusion model, the limitation of drift-diffusion-model is derived.

Simplification of the ICCG method for matrix inversion in semiconductor device simulation

On presente une simplification de l'algorithme ICCG (Gradient conjugue de CHOLESKI incomplet) pour l'inversion de matrices dans la simulation des dispositifs semiconducteurs. Des methodes rapides, basees sur la relation fondamentale d'un vecteur solution avec son erreur residuelle (RE) et son erreur conjuguee (CE) sont developpees

An adaptive finite element scheme using multi-grid method for magnetostatic problems

A multigrid solver is developed to reduce computing time in the adaptive finite-element scheme. The meshes generated by the adaptive scheme can be directly used as multigrids for the computation. Elements in the adaptively generated grids are concentrated around the singular points, which makes the use of simple injection for restriction impossible. To overcome this problem, a weighted restriction is introduced. A magnetostatic field problem with a high degree of singularity is chosen as a case study. The multigrid method with weighted restriction reduces the computing time considerably compared with the well-known ICCG method. The computing time for problems where number of nodes is of the order of 10000 is reduced to 30%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

ICCG and related methods for 3D problems on vector computers

If the recurrencies in the ICCG preconditioning for 3D problems are vectorized by the same techniques as used for 2D problems, then the vector lengths in the critical part of the algorithm are O ( N 1/3), N being the order of the linear system to be solved. Since in practical situations N 1/3 is no large, this puts restrictions on the overall performance. In this paper we consider also techniques that lead to larger vector lengths. Actual results, obtained on Japanese supercomputers, are reported.

Two Multigrid Methods for Three-Dimensional Problems with Discontinuous and Anisotropic Coefficients

The subject of this paper is two multigrid methods for the numerical solution of \[ - \nabla \cdot (D(x,y,z)\nabla U(x,y,z)) + \sigma (x,y,z)U(x,y,z) = F(x,y,z) \] in a bounded region $\Omega $ of $R^3 $, where $D = (D^1 ,D^2 ,D^3 ),D^i $ is positive, $i = 1,2,3$, and $D^i ,\sigma $, and F are allowed to be discontinuous across internal boundaries of $\Omega $. The first method differs in two important ways from previously considered multigrid methods for such problems; first, if standard coarsening is used, then anisotropic problems require plane relaxation to obtain a good smoothing factor; for problems with discontinuous coefficients, this was previously done with an ICCG method; here it is done with a two-dimensional multigrid method. Second, a slightly different form of interpolation is used which improves performance for nearly singular problems. Previously considered multigrid methods for problems with discontinuous coefficients have defined the coarse grid operators by Galerkin coarsening; in the second method, such coarsening is also used but with auxiliary intermediate grids obtained by semicoarsening successively in each of the three independent variables; this artifice simplifies coding considerably and results in comparable convergence.

Investigation of numerical algorithms in semiconductor device simulation

The algorithms used in semiconductor device simulation are investigated. Inversion algorithms, such as SOR, SI, generalized ICCG and Crout methods are compared in terms of convergency and required computer resources for various devices and bias conditions. For linearization of the basic equations, a quasi-coupled method is also compared with Gummel's conventional decoupled method. Numerical experimentation shows that even the SOR method, which has the slowest convergency among these algorithms, efficiently provides good results when used properly. Moreover, the quasi-coupled method is also effective in linearizing the basic equations for transient analysis or high bias conditions without a significant increase in the required memory. Consequently, a properly used simulator having several algorithms is shown to be necessary for two- and three-dimensional analysis. Furthermore, guidelines for applying these numerical algorithms effectively are described in detail.

Large scale structural analysis by a supercomputer. (Application of the ICCG method to finite element analysis).

Recently, with the rapid progress of computer technology, there is a growing need for large scale non-linear finite element analyses. However, These calculations take a lot of time and have large storage requirements. The authors have applied the ICCG method, which is one of the iterative solutions, to the three dimensional finite element analysis by supercomputer. Using the ICCG method, large problems with over 10 000 nodes have been solved in a short computational time and with good accuracy.

反復計算法の気流計算への応用

This paper describes the reduction of computation time of a large sparse linear equations obtained by discretization of a three-dimensional Poisson's equation using the finite difference method. The equation is induced from wind field calculations, which are needed for evaluation of environmental consequences due to radioactive effluents.Various iterative methods, such aS ICCG, MICCG, ILUCR and MILUCR methods, are applied to solving linear equations and are compared with SOR method. The optimum value of the acceleration factor of SOR method can be obtained numerically according to atmospheric stability for each nuclear site, and the iterations are minimized by using this optimum value.The computation time for MICCG or MILUCR method is a half of that for SOR method. The ILUCR method is better than SOR method, because it does not use acceleration factor and the computation time is shorter. The use of vector computer drastically reduces the computation time, and all the iterative methods are applicable. A scalar computer, however, favors the use of MILUCR or MICCG methods because of a half of the computation time for SOR method.

Application of ICCG Method to Numerical Solutions of Few-Group Neutron Diffusion Equations

KEYWORDS: few-group neutron diffusion equationmatrix solutionconjugate gradient methodincomplete Choleski decompositioninner iterationconvergencyalgorithmseigenvalues

Application of ICCG method to numerical solutions of few-group neutron diffusion equations.

Application of ICCG method to numerical solutions of few-group neutron diffusion equations.

Modification of ICCG method for application to semiconductor device simulators

A high-speed iterative solution method for linear equations is proposed, which consists essentially of modifying the ICCG method to enable a processing of slightly asymmetrical coefficient matrices usually encountered in simulation problems pertaining to semiconductor devices. The new algorithm, applied to several two- and three-dimensional device simulators, has brought about a remarkable reduction in computation time.