![]() Since the computation of the truncation error is problematic we consider the relative local truncation error We can see that can be regarded as the correction of so that the solution of the fine-grid equation will be the exact solution Where is the exact solution of the original equation ![]() The coarse grid correction is given by the difference of coarse and fine grid solution. Suppose we have a nonlinear smoother and the initial solution is already sufficiently smoothĪfter smoothing steps the defect equation is put onto the coarse grid To do this we need a non linear relaxation procedure to smooth errors for approximating corrections on coarser grids.Īnd in a discetized form on a regular grid with mesh size h as Multigrid can be applied directly to nonlinear problems. Multigrid for Nonlinear Problems (Brand's Full Approximation Storage (FAS)) By Full Multigrid Cycle we start on the coarsest grid solving the equation excactly. The main difference between Multigrid Cycles and Full Multigrid Cycles is the start of the algorithm. Then we get a new improved approximate solutionĪdd correction from coarse grid to fine-grid solution In the next step we have to approximate the discretized operatorĪnd solve using one of a relaxation method described above (Jacobi or Gauß-Seidel) Suppose we are trying to solve linear elliptic Problem (Poisson's equation)ĭiscretize equation on a uniform grid with mesh size h Even nonlinear equations can be solved with comparable speed. The multigrid methods can solve general elliptic equations with nonconstant coefficients with hardly any loss in efficiency. Practical multigrid methods can solve elliptic PDEs discretized on N grid points in O(N) operations. Where is easily invertible an is the remainder.įor the Jacobi method the easily inertible part is given by Relaxation methods make immediate use of the structure of the sparse matrix After dicretization we can represent our model as the equation. Relaxation Methods are used to perform smoothing operations by Multgrid Methods. Resulting equation follows from Debye-Hückel theory We describe a protein as a bunch of point charges in some kind of insulator (fat). The Poisson-Boltzmann equation models the energy constribution due to screening effects due to exterior counter ions. The intramolecular dynamics is simulated using the HP lattice model. Transfer Operators (prolongation and restriction)įinite difference and multigrid methods for the Poisson-Boltzmann equation for accelerating Monte-Carlo simulations of simple models for protein folding.Funktion: test_grid_transfer_implementation.Wrapper Function: _MG_reference_solution.Wrapper Function: _restriction_unit_test.Wrapper Function: _prolongation_unit_test.Kernel Function: prolongation_unit_test.Wrapper Function: _gauss_seidel_unit_test.Declarations of Kernel Wrapper Functions.Release device memoryĭevice memory is deallocated in the same programmatic manner as host allocated arrays.The step-12 tutorial program Table of contents The implicit copy from the device to the host will block until the kernel is completed. We launch our kernel with a modified Fortran subroutine syntax that lets us specify the grid and block sizes. Each thread takes care of one element of c Each thread evaluates one copy of the kernel. The total number of threads is ( blockdim) * ( griddim). When we launch a kernel we specify the number of threads per block( blockdim) and number of blocks per grid( griddim). The kernel is the heart of our CUDA code. ! Sum up vector c and print result divided by n, this should equal 1 within error Id = (blockidx%x-1)*blockdim%x + threadidx%x Each thread takes care of one element of cĪttributes(global) subroutine vecAdd_kernel(n, a, b, c) Please direct any questions or comments to vecAdd.cuf The full source can be viewed or downloaded from the OLCF GitHub. Consider this a CUDA Fortran ‘Hello World’. This tutorial shows a minimal conversion from our vector addition CPU code to PGI CUDA Fortran. Home / Tutorials / Cuda Fortran Vector Addition
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