Abstract :
The author extends previous work to discretizations, over tetrahedral and hexahedral meshes, of functionals which often arise in the analysis of magnetoquasistatic problems. For natural boundary conditions, exact formulae for the number of degrees of freedom and the number of nonzero entries in the stiffness matrix are given in terms of the number of nodes in the mesh, the number of elements, the number of boundary nodes, and the Euler characteristic. From this, explicit formulae for the number of FLOPS (floating point operations) per conjugate gradient iteration are given for node- and edge-based vector interpolation on hexahedral and tetrahedral meshes. Thus, formulae for quantities required for the comparison and validation of finite element codes are given
Keywords :
conjugate gradient methods; finite element analysis; interpolation; magnetostatics; Euler characteristic; conjugate gradient iteration; discretizations; edge-based vector interpolation; finite element codes; hexahedral meshes; magnetoquasistatic problems; natural boundary conditions; node-based vector interpolation; number of FLOPS; number of degrees of freedom; number of nodes; number of nonzero entries; stiffness matrix; tetrahedral meshes; three dimensional vector finite element interpolation schemes; Arithmetic; Boundary conditions; Character generation; Equations; Finite element methods; Interpolation; Magnetic analysis; Mesh generation;
