Authors:Alban Kuriqi, Mehmet Ardiçlioglu, and Ylber Muceku
, Daneshmand F.
Three-dimensional smoothed fixed grid finiteelementmethod for the solution of unconfined seepage problems , Finite Elements in Analysis and Design , Vol. 64 , 2013 , pp. 24 – 35
method (FVM) [ 34 ] and the FiniteElementMethod (FEM) [ 35 ]. In this work, we will choose this last method as a method of solving problems of irregular structures in elevation. The concept of this method is used for numerical analysis wherein the model
A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations
arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the
recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited
to parallel computation.
Several nonlinear simulations of concrete and reinforced concrete slabs are performed using a layered model. Two Drucker-Prager criteria are employed to form a concrete plasticity model that is used for simulating the plastic yielding of layers. Moreover, an interaction with elastic Winkler-Pasternak subsoil model is considered for the case of a reinforced concrete foundation slab that is subjected to a concentrated loading force. All computations are done by the SIFEL solver using finite element method.
A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in  and  for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well.
The minimum degree ordering is one of the most widely used algorithms to preorder a symmetric sparse matrix prior to numerical factorization. There are number of variants which try to reduce the computational complexity of the original algorithm while maintaining a reasonable ordering quality. An in-house finite element solver is used to test several minimum degree algorithms to find the most suitable configuration for the use in the Finite Element Method. The results obtained and their assessments are presented along with the minimum degree ordering algorithms overview.
A geometric multigrid method for the efficient solution of time-harmonic 3-D eddy-current problems is presented. A finite element method with a scalar potential and a vector potential is used to describe the problem. Numerical examples show that using the right smoother in the multigrid, a good convergence of solutions, which does not deteriorate for bad quality meshes can be obtained. The computation time for solving the eddy-current problem of the multigrid method is much faster than that of the conjugate gradient method with incomplete Cholesky factorization as preconditioner.