In this paper we propose a method for conducting stochastic collocation on arbitrary sets of nodes. To accomplish this, we present the framework of least orthogonal interpolation, which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions. These interpolation polynomials are constructed as a subspace of the family of orthogonal polynomials...

1. INTRODUCTION This paper presents a finite-element collocation scheme for simulating variably saturated flows in two space dimensions. The scheme is an extension of a mass conserving one-dimensional formulation presented earlier [Allen and Murphy, 1985). The present exposition gives a complete description of work reported more briefly in the work by Murphy and Allen [1986]. Among the key feat...

We consider the numerical solution of the problem of time-harmonic acoustic scattering in two dimensions by a sound soft convex polygon. Standard boundary or finite element methods with piecewise polynomial approximation spaces have a computational cost that grows at least linearly with respect to the frequency of the incident wave. By including in the approximation space the products of plane ...

The utility of orthogonal collocation methods in the solution of optimal control problems relating to Formula One racing is demonstrated. These methods can be used to optimise driver controls such as the steering, braking and throttle usage, and the optimisation of vehicle parameters such as aerodynamic down force distributions. Of particular interest is the optimal usage of energy recovery sys...

The cutting is an important machining technology, in which is belong to nonlinear large deformation, involving material nonlinear, geometry nonlinear and original bug, the thermal energy coupling question, and the nonlinear boundary condition, and so on. For the processing of metal cutting, using the large-scale commercial finite element theory, the coupling finite element model is established ...

In the work of solving a uniformly elliptic differential equations Au := − u+ a1ux + a2uy + a0u = f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix whe...

It is well known that the use of conventional discrete numerical methods of analysis (FEM and BEM) in the solution of Helmholtz and elastodynamic wave problems is limited by an upper bound on frequency. The current work addresses this problem by incorporating the underlying wave behaviour of the solution into the formulation of a boundary element, using ideas arising from the Partition of Unity...

This paper is concerned with the identification of the geometrical structure of the boundary shape for a two-dimensional boundary value problem. The output least square identification method is considered for estimating partially unknown boundary shapes. A numerical parameter estimation technique using the spline collocation method is proposed. lThis research was supported by the National Aeron...