1,721,064 research outputs found
Notes on Linear FEM and MHFE
No full textRapporto Tecnico CS-2005-9, Dipartimento di Informatica, Universita' "Ca' Foscari" di Venezi
Meshless Petrov--Galerkin Methods
No full textRapporto Tecnico CS-2007-7, Dipartimento di Informatica, Universita
A DMLPG Refinement Technique for 2D and 3D Potential Problems
No full textMeshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations (PDE). MLPG techniques are nowadays used for solving a huge number of complex, real–life problems. While MLPG aims to approximate the solution of a given differential problem, its “dual” Direct MLPG (DMLPG) technique relies upon approximating linear functionals. Assume adaptive methods are to be implemented. When using a mesh–based method, inserting and/or deleting a node implies complex adjustment of connections. Meshless methods are more apt to implement adaptivity, since they does not require such adjustments. Nevertheless, ad–hoc insertion and/or deletion algorithms must be devised, in order to attain a good accuracy. In this paper we introduce a fresh refinement technique for DMLPG methods. Nodes are inserted in a discretization cloud where the local variation in the solution is supposed to be “large”. The variation is estimated using the (local) Total Variation (TV). DMLPG allows to directly estimate the partial derivatives, in order to compute the TV. MLPG must rely upon approximating the derivatives of the shape functions, hence MLPG refinement results to be more involved than its DMLPG counterpart. We show that our DMLPG refinement procedure allows one to efficiently solve a given diffusion problem whose solution undergoes large variations on a small portion of the domain. The accuracy afforded by a fine uniform cloud can be attained by using far less non–uniformly arranged nodes
Solving Nonlinear Differential Equations
Full text linkMathematica is great in solving analytically linear differential equations. It is also a good companion for computing numerical solutions to non–linear equations. We attack the reduced–gravity, shallow–water equation (RSE) problem. We compare the analytical solution to our problem without friction to the numerical solution obtained either with Mathematica or via Matlab. We exploit Mathematica ability in solving systems of non-linear Ordinary Differential Equations, on the way to identify some analytical solution to RSE when friction is non-negligible
Conversion of Data Between Triangular and Rectangular Meshes for Pre- and Post- Processing in Hydrologic Problems
No full text
A Modified Conjugate Gradient Method for the Solution of Sparse Linear Systems on Microcomputers
No full textA Modified Conjugate Gradient scheme to solve sparse linear systems with positive definite coefficient matrices has been implemented on a microcomputer. A discussion of its mathematical properties shows that it is a good algorithm for small computers. The representation of the data used in the implementation requires the storage only of the non zero elements of the coefficient matrix, thus attaining a great saving of memory space. Test examples are given for matrices arising from the finite element analysis of structural problems, and the performance of the Conjugate Gradient scheme is compared with that of other algorithms commonly used to solve sparse linear systems on microcomputers
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