Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Falgout, Robert D."'
Fast Iterative Solver For Neural Network Method: II. 1D Diffusion-Reaction Problems And Data Fitting
This paper expands the damped block Newton (dBN) method introduced recently in [4] for 1D diffusion-reaction equations and least-squares data fitting problems. To determine the linear parameters (the weights and bias of the output layer) of the neura
Externí odkaz:
http://arxiv.org/abs/2407.01496
The discretization of the deep Ritz method [18] for the Poisson equation leads to a high-dimensional non-convex minimization problem, that is difficult and expensive to solve numerically. In this paper, we consider the shallow Ritz approximation to o
Externí odkaz:
http://arxiv.org/abs/2404.17750
As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a significant bo
Externí odkaz:
http://arxiv.org/abs/2208.12629
Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute patterns to
Externí odkaz:
http://arxiv.org/abs/2205.14273
As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes are a significant bott
Externí odkaz:
http://arxiv.org/abs/2201.10441
Autor:
Hessenthaler, Andreas, Falgout, Robert D., Schroder, Jacob B., de Vecchi, Adelaide, Nordsletten, David, Röhrle, Oliver
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorith
Externí odkaz:
http://arxiv.org/abs/2105.00305
Autor:
De Sterck, Hans, Falgout, Robert D., Friedhoff, Stephanie, Krzysik, Oliver A., MacLachlan, Scott P.
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in modern high-performance computing environments. While these techniques
Externí odkaz:
http://arxiv.org/abs/1910.03726
Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication
Externí odkaz:
http://arxiv.org/abs/1906.10575
Autor:
Adams, Michael P., Adams, Marvin L., Hawkins, W. Daryl, Smith, Timmie, Rauchwerger, Lawrence, Amato, Nancy M., Bailey, Teresa S., Falgout, Robert D., Kunen, Adam, Brown, Peter
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on a class of grids in 2D and 3D Cartesian geometry that are regular at a coarse level but arbitrary within the coarse blocks. We describe these algorithms a
Externí odkaz:
http://arxiv.org/abs/1906.02950
Autor:
Guzik, Stephen M., Christopher, Joshua, Walters, Sean, Gao, Xinfeng, Schroder, Jacob B., Falgout, Robert D.
Publikováno v:
In Computers and Fluids 15 July 2023 261