Meshfree Methods Over the past several decades mesh-based computational schemes (e.g. finite element (FE) /finite volume (FV) techniques) have found wide application as reliable analysis tools for a large class of boundary value problems on geometrically complex domains. Central to such techniques is the process of “mesh generation” where the computational domain is divided into subdomains (called “elements"). The generation of a “good quality” computational mesh, however, is quite a challenging task. A relatively undistorted mesh is required for reasonably accurate solutions. Not only is mesh generation expensive, but also the error in computing the Jacobian on a distorted mesh grows rapidly with increase in mesh distortion and the solution becomes spurious unless remeshing is performed. Remeshing is time consuming and may lead to reduction of accuracy of the solution due to numerical diffusion and problems of satisfying required conditions on transferred fields when state variables are mapped from one mesh to the other. For problems involving change of mesh topology (e.g. dynamic crack growth, fracture/fragmentation) remeshing has to be performed very frequently and this results in increased numerical errors and computational time. It is therefore quite natural that there is considerable interest in developing computational schemes that do not use a mesh and the discretization is based solely on a set of nodal points. Some of the other advantages of such a “meshfree” technique are: (1)    It is easier to generate approximation spaces having higher order continuity. (2)    Handling of adaptivity is simpler. (3)    It is possible to embed a priori estimates of solutions of governing partial differential equations in neighborhoods of singularities to obtain faster convergence. (4)    There is a drastic simplification of the data structure associated with a given discretization. However, existing meshfree methods are computationally expensive compared to the traditional finite element methods. Our research has been aimed at developing computationally efficient meshfree methods that are stable and realibale for general use and to provide an automated computational enviroment that is capable of obtaining gemoetry information directly from solid modleing packages and performing discretization using nodal points only.  PROJECTS Method of Finite Spheres (MFS) Octree Partition of Unity Method (OctPUM) Automatic meshfree domain disctretization methods Efficient numerical integration Genetic Algorithm-based lookup table approach for numerical integration Scalable and localizable enrichment strategies Stability analysis of meshfree methods using the numerical inf sup test Solutioon of hyperbolic problems Solution of nonlocal plasticty problems SPONSORS       INVESTIGATORS     Suvranu De