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An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks
{\it Critical slowing down} associated with the iterative solvers close to
the critical point often hinders large-scale numerical simulation of fracture
using discrete lattice networks. This paper presents a block circlant
preconditioner for iterative solvers for the simulation of progressive fracture
in disordered, quasi-brittle materials using large discrete lattice networks.
The average computational cost of the present alorithm per iteration is , where the stiffness matrix is partioned into
-by- blocks such that each block is an -by- matrix, and
represents the operational count associated with solving a block-diagonal
matrix with -by- dense matrix blocks. This algorithm using the block
circulant preconditioner is faster than the Fourier accelerated preconditioned
conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing
down} that is especially severe close to the critical point. Numerical results
using random resistor networks substantiate the efficiency of the present
algorithm.Comment: 16 pages including 2 figure
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Convective, Diffusive Effects on Magnetic Fields and Eddy Current in Compulsators
Compulsators are being designed at ever increasing energies and energy densities and are required to deliver energy to the load in less than 10 ms. These require high speeds of operation and dense spacing of conductors. Diffusion of magnetic fields into the conductors and the formation of nonuniform, time-dependent distribution of eddy currents become dominant design considerations due to their major mechanical, thermal, and thermodynamic impact. A semi-analytical method has been developed for the two-dimensional analysis of field diffusion and eddy currents in high speed rotary machines to aid design decisions. Analytical results for fields are utilized and computations are restricted to the conductor domains alone. The semi-analytical method has been tested with two conductors (one in the stator and one in the rotor rotating at high speed). The resulting distributions of fields and eddy currents are presented.Center for Electromechanic
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