1,721,001 research outputs found
A second order cell method for Poisson's equation
No full textThe Cell Method, similar to the Finite Integration Technique, is a well-established numerical method for the solution of field problems, however an often raised criticism is that it is limited to constant fields within elements. In this paper we show that for the case of Poisson's equation the Cell Method can be extended to the second order convergence. Numerical results showing the order of convergence of the method are presente
Tree-cotree implicit condensation in magnetostatics
No full textA tree-cotree decomposition of the graph associated with a finite-element mesh allows the implementation of a method which is equivalent to a mixed one but which gives rise to a symmetric positive definite linear system with a reduced number of unknowns. We will refer to this method as TCIC (Tree-Cotree Implicit Condensation). A possible preconditioning scheme for the resulting linear system is presented and the effect of the choice of particular tree-cotree decompositions is discussed from the point of view of numerical performanc
An adaptive mixed formulation for 3D magnetostatics
No full textAn enhanced version of a mixed field-based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation minimises the residual of the constitutive equation, and exactly imposes Maxwell’s equations with Lagrange multipliers. Finite elements satisfying the physical continuity properties for both the magnetic and the magnetic induction fields are used in the numerical approximation. The possibility of decoupling the formulation in two separate sets of equations is discussed. A preconditioned iterative method to solve the final algebraic linear system is presented. Finally, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure
Mixed finite element methods and tree-cotree implicit condensation
No full textMixed methods are widely used for the finite element analysis of differential problems. From a computational point of view, however, the increase in the number of variables from that of the original problem and the properties of the resulting matrices often make a direct implementation of these formulations inadvisable. In this paper, the mixed formulation of Dirichlet’s problem for the Laplace operator, discretised using lowest degree Raviart–Thomas elements will be considered as an example. A tree-cotree decomposition of the graph associated with the mesh allows the implemen- tation of an equivalent method, which significantly reduces the number of degrees of freedom and gives rise to a symmetric positive definite linear system. We will refer to this novel method as tcic (Tree-Cotree Implicit Condensation). Numerical results will be presented, and the possibility of extending the proposed method to other cases will be discussed
Equivalent Source Methods for 3D Force Calculation with Nodal and Mixed FEM in Magnetostatic Problems
No full textImplementation of Surface Impedance Boundary Conditions in the Cell Method via the Vector Fitting Technique
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