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This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads.…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded…
The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for…
Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…