We present a collocatIon method based on piecewise cubic polynomials I In C for solving various Integral and differential equatIons. Two new methods for handling curved boundaries are discussed based on collocation and discrete least-squares. Finally, a summary of the properties of the collocation method Is given which IndIcates the simplicity, flexlbl1fty, efficiency, and generality of the met...

In this paper we present a new method of automatic collocation identification. Collocation is an important relation between words, which is widely used, among others, in information retrieval tasks. Over the last years, many methods of automatic collocation acquisition from text corpora have been proposed. The approach described in this paper differs from the others by focusing on domain colloc...

A meshfree method and (the related) a specified crack growth algorithm are used to simulate plugging fracture during high-speed impacts. In particular, we are simulating ballistic penetration of a steel plate, which is a ductile failure process involving projectile and target collision, contact, and subsequent projectile penetration companied plugging fracture inside steel plate. We have develo...

This paper describes the use of WordNet in a new technique for collocation extraction. The approach is based on restrictions on the possible substitutions for synonyms within candidate phrases. Following a general discussion of collocations and their applications, current extraction methods are briefly described. This is followed by a detailed description of the new approach and results and eva...

Article history: Received 15 December 2010 Received in revised form 21 April 2011 Accepted 24 April 2011 Available online 4 May 2011

Here are three short stories on meshless methods using kernel techniques: • Any well–posed linear problem in the native space NΦ of a symmetric (strictly) positive definite kernel Φ can be successfully solved by symmetric meshless collocation. This applies to a large variety of standard linear PDE problems. • Relaxing interpolation conditions by allowing some small absolute error can significan...

In this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. The challenges satisfying Dirichlet meshfree and particle methods are well-known. This issue is also pertinent the development of physics informed networks (PINN) for solution partial differential equations. We geometry-aware trial functions artific...