Monotone iterations for differential problems

Monotone Iterations for Eliptic Variational Inequalities

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Preconditioning Waveform Relaxation Iterations for Differential Systems

We discuss preconditioning and overlapping of waveform relaxation methods for sparse linear diierential systems. It is demonstrated that these techniques signiicantly improve the speed of convergence of the waveform relaxation iterations resulting from application of various modes of block Gauss-Jacobi and block Gauss-Seidel methods to diierential systems. Numerical results are presented for li...

Schwarz Iterations for Symmetric Positive Semidefinite Problems

Convergence properties of additive and multiplicative Schwarz iterations for solving linear systems of equations with a symmetric positive semidefinite matrix are analyzed. The analysis presented applies to matrices whose principal submatrices are nonsingular, i.e., positive definite. These matrices appear in discretizations of some elliptic partial differential equations, e.g., those with Neum...