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A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
Productivity languages such as NumPy and Matlab make it much easier to implement data-intensive numerical algorithms. However, these languages can be intolerably slow for programs that don't map well to their built-in primitives. In this…
Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
Major chip manufacturers have all introduced multicore microprocessors. Multi-socket systems built from these processors are used for running various server applications. However to the best of our knowledge current commercial operating…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
Mining large graphs for information is becoming an increasingly important workload due to the plethora of graph structured data becoming available. An aspect of graph algorithms that has hitherto not received much interest is the effect of…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We describe a strategy for code modernisation of Gadget, a widely used community code for computational astrophysics. The focus of this work is on node-level performance optimisation, targeting current multi/many-core IntelR architectures.…
We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…
For challenging state estimation problems arising in domains like vision and robotics, particle-based representations attractively enable temporal reasoning about multiple posterior modes. Particle smoothers offer the potential for more…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…
Multicore architectures dominate today's processor market. Even though the number of cores and threads are pretty high and continues to grow, inherently serial algorithms do not benefit from the abundance of cores and threads. In this…
Over the past few years, there has been an increased interest in including FPGAs in data centers and high-performance computing clusters along with GPUs and other accelerators. As a result, it has become increasingly important to have a…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…
We present a monolithic $hp$ space-time multigrid method for tensor-product space-time finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm…