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12 processors alternate implicit methods analysis problems need approximately assigned degree coefficients communication computation flow computational speed CONCURRENT IMPLEMENTATION concurrent processing computer Concurrent Processing Hardware cycles cyclic reduction degree of freedom denoted direct method direct technique Element Machine FEM example transient test experimental MIMD computer finite difference Finite Element Machine flag network Fulton George Washington University global bus global convergence heat transfer analysis heat transfer equations heat transfer problem Instruction Multiple Data iterations iterations iterations iterative method iterative technique J+1 rows Langley Research Center large-order matrix MIMD computer called Multiple Data MIMD Multiple Instruction Multiple n processors NASA Langley Research Newton-Raphson NONLINEAR PROBLEMS number of iterations number of processors parallel computers PASLIB Performing Organization Processor n/2 Ransom reduce relative speedups Research Center Hampton shown in Figure solve Storaasli system of equations technique is faster temperatures are calculated thermal transfer analysis problems tridiagonal equations tridiagonal system varied number XXj+1