## High-Performance Computing in Engineering: Applications to Partial Differential Equations |

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algorithm BDTUD block boundary conditions boundary element method Brebbia calculated communication conjugate gradient method considered control volume convergence rate CRAY Y-MP Davies defined described differencing discretization distributed memory domain driven cavity flow dynamic efficiency Engineering Figure finite difference finite element fluid flux formulation FORTRAN function Gaussian elimination grid point increase integral equation inviscid linear system Lobry MAC/BDTUD massively parallel matrix mesh Mflops multigrid method multiprocessor natural convection Navier-Stokes equations nonlinear number of iterations number of processors numerical diffusion obtained operations parabolic parallel complexity parallel computers parallel implementation parallel processing particle PDEs performance PISO potential Rayleigh Rayleigh wave Reynolds number sequential SIMD simulations solution solver solving space space-parallel sparse matrix speed-up step storage strategy supercomputers symmetry system of equations Table Theoretical Peak three-dimensional time-parallel multigrid time-steps tion transputer two-dimensional V-cycle values vector length velocity vibration viscoelastic workstation