Recently the hp version of the finite element method, in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials, has received increasing attention. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method, such as multigrid. An intriguing notion is to use the values o...

Adaptive Optimization Hyperparameter tuning is a big cost of deep learning. Momentum: a key hyperparameter to SGD and variants. Adaptive methods, e.g. Adam1, don’t tune momentum. YellowFin optimizer • Based on the robustness properties of momentum. • Auto-tuning of momentum and learning rate in SGD. • Closed-loop momentum control for async. training. Experiments ResNet and LSTM YellowFin runs w...

In this paper an algorithm is presented to store and process fully adaptive computational grids requiring only a minimal amount of memory. The adaptive grid is specified by a recursive bisection of triangular grid cells. The cells are stored and processed in an order specified by the Sierpinski space-filling curve. A sophisticated system of stacks is used to ensure cache-efficient access to the...

Existing map deformation techniques are mainly based on uniform grids and can be insufficient for real-time demands. For higher flexibility of allocating resolutions, we propose to use a content-aware non-uniform grid. Our contentaware non-uniform grid leads to adaptive resolutions on the map deformation. This adaptive approach results in both higher road deformability and performance. We imple...

We present an adaptive fast multipole method for solving the Poisson equation in two dimensions. The algorithm is direct, assumes that the source distribution is discretized using an adaptive quad-tree, and allows for Dirichlet, Neumann, periodic, and free-space conditions to be imposed on the boundary of a square. The amount of work per grid point is comparable to that of classical fast solver...

Finite-volume discretization schemes for viscous fluxes on general grids are compared using node-centered and cell-centered approaches. The grids range from regular grids to highly irregular grids, including random perturbations of the grid nodes. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes (a node-...

In this paper we apply the finite difference method on adaptive sparse grids [9] to the simulation of turbulent flows. This method combines the flexibility and efficiency of finite difference schemes with the advantages of an adaptive approximation by tensor product multiscale bases. We shortly discuss the method. Then, we present numerical results for a simple linear convection problem for a v...

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution prin...

This paper describes an adaptive, unstructured mesh generator, which can be used for discretizing regional and global domains for geophysical flow simulations in general, and atmospheric flow simulations in particular. The global mesh generator is a part of the Operational Multiscale Environmental model with Grid Adaptivity (OMEGA) System. For a physically complex and computationally intensive ...

This paper argues that the assumption of end-to-end QoS provision for use in Grid based applications is unsafe. We present an architecture which provides an adaptive QoS service for GRID applications which are prepared to adapt rather than assume the best and then suffer the worst. This is particularly relevant to Internet based GRIDs. An example application from the field of collaborative lear...