Improved successive constraint method baseda posteriorierror estimate for reduced basis approximation of 2D Maxwell's problem

Successive Constraint Method in the Collocation Reduced Basis Method

Parametric Partial Differential Equations arise in many areas of applied mathematics and the natural sciences. Efficient numerical simulations to these types of problems across a wide range of parameter values presents a stiff computational challenge. The Reduced Basis Method presents an efficient scheme for solving these types of problem. Utilization of this method however, depends on the know...

A Seamless Reduced Basis Element Method for 2d Maxwell’s Problem: an Introduction

We present a reduced basis element method (RBEM) for the time-harmonic Maxwell’s equation. The RBEM is a Reduced Basis Method (RBM) with parameters describing the geometry of the computational domain, coupled with a domain decomposition method. The basic idea is the following. First, we decompose the computational domain into a series of subdomains, each of which is deformed from some reference...

0 One Form of Successive Approximation Method and Choice Problem

A Novel Successive Approximation Method for Solving a Class of Optimal Control Problems

This paper presents a successive approximation method (SAM) for solving a large class of optimal control problems. The proposed analytical-approximate method, successively solves the Two-Point Boundary Value Problem (TPBVP), obtained from the Pontryagin's Maximum Principle (PMP). The convergence of this method is proved and a control design algorithm with low computational complexity is present...

A Successive Minima Method for Implicit Approximation

This paper is concerned with the problem of approximating a collection of unorganized data points by an algebraic tensor-product B-spline curve. The implicit approximation to data points would be ideally based on minimizing the sum of squares of geometric distance. Since the geometric distance from a point to an implicit curve cannot be computed analytically, Sampson distance, which is the firs...