On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

On Solvability of a Boundary Value Problem for Singular Integral Equations

This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05     

Modelling and optimal control of coupled structural acoustic systems with piezoelectric elements

We construct a model of a shell with piezoelectric elements (patches) that take into account the mutual influence of deformations and electric fields. Coupled problems for the shell with piezoelectric patches and an acoustic field, are studied and results on the existence and the uniqueness are obtained. For this system we consider an optimal control problem on noise attenuation and obtain results on the existence, the uniqueness, necessary and sufficient conditions of optimality. Copyright © 2003 John Wiley & Sons, Ltd.     

A note on a characterization of P-matrices

In this note we show that the characterization results for P-matrices due to K.G. Murty and A. Tamir which state that a given square matrixM of ordern is a P-matrix if and only if the linear complementarity problem (q, M) has a unique solution for allq in a specified finite subset of ⁿ depending onM are incorrect whenn > 3.Research supported by Dr. K.S. Krishnan (DAE) fellowship for research in Mathematics and Computer Science, Bombay, India.     

气体放电击穿过程的物理和数值研究

本文对低气压（１０＾－２Ｐａ）热阴极气体放电的击穿过程给出了物理描述和相应的双流体数学型，并发展了一种选择和调整未知初始条件的有效算法，可以通过伴随试射法得到对初始条件十分敏感的非线性两点边值常微分方程组的数值解，从而给出这类气体放电中击穿过程的定量描述。     

透平级S_2流面内的反问题湍流计算

本文发展了应用湍流流函数方程计算湍流流场的方法。计算了扭曲叶片Ｓ２流面的湍流流场．在非正交曲线坐标可压湍流方程组中包含了以无量纲形式表示的能量方程，熵方程和Ｋ－ε湍流模型方程。固壁边界上采用了壁函数方程。通过计算得到了透平级内部的湍流流动合理的收敛解。此方法可以通过调节子午通道的形状及环量的大小分布来防止流动中负速度的出现，为高效透平级的设计提供了一种新的途径。     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

一类基于变量分离的稳定化混合有限元方法

Based on a seperated model for saddle-point problems, we develop a new sta-bilized mixed finite element method. Such a model consists of two subproblems with respect to the primal and the dual variables, respectively. We show that the new method is coercive and that optimal error bounds hold. As an application,the nearly incompressible elastic problem is analyzed with our method.