numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. this study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. the crack tip element and a higher order boundary displacement collocation techn...

Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium in non-periodic space. The concentration is treated by a characteristics collocation method, while the pressure is treated by a finite element collocation method. Optimal order estimates in L2 is derived.

We present greedy unsymmetric collocation schemes for solving linear elliptic partial differential equations using radial basis functions. The proposed approach circumvents the ill-conditioning problem associated with the standard collocation technique and enables the efficient solution of problems requiring a large set of collocation points. Numerical studies indicate that the accuracy of gree...

This report evaluates the impact of using a novel collocation segmentation method for phrase extraction in the standard phrase-based statistical machine translation approach. The collocation segmentation technique is implemented simultaneously in the source and target side. The resulting collocation segmentation is used to extract translation units. Experiments are reported in the Spanish-toEng...

This document discusses accuracy of the collocation technique we employ to calculate the velocity field in ambient inviscid fluid above an interface swollen by a denser source fluid.

This report evaluates the impact of using a novel collocation segmentation method for phrase extraction in the standard phrase-based statistical machine translation approach. The collocation segmentation technique is implemented simultaneously in the source and target side. The resulting collocation segmentation is used to extract translation units. Experiments are reported in the Spanish-toEng...

The effect of diverse sources of uncertainties and the intrinsically multi-scale nature of real-world physical systems poses a considerable challenge to analyze such systems. Such phenomena are particularly critical in material systems wherein microstructural variability and randomness at lower scales have a significant impact on the behavior of the system. Towards this goal, some of our accomp...

A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the ...