Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method [43, 1, 31, 30] has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method [28, 40, 33], primarily developed for solving parametric systems, has been recently used to deal with stochastic problems [7, 6]. In this work, we aim at comparing the performance of the two methods when applied t...

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...

Reduced Basis Collocation Methods for Partial Differential Equations with Random Coefficients

The sparse grid stochastic collocation method is a new method for solving partial differential equations with random coefficients. However, when the probability space has high dimensionality, the number of points required for accurate collocation solutions can be large, and it may be costly to construct the solution. We show that this process can be made more efficient by combining collocation ...

Stochastic Reduced Basis Methods

THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.