Related papers: Block-Structured Adaptive Mesh Refinement Algorith…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids…
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all…
Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on…
Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
Adaptive Mesh Refinement (AMR) is becoming a prevalent data representation for scientific visualization. Resulting from large fluid mechanics simulations, the data is usually cell centric, imposing a number of challenges for high quality…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and medical imaging. Parameter estimation is commonly phrased as a PDE-constrained optimization problem that can…
Machine learning with big data often involves large optimization models. For distributed optimization over a cluster of machines, frequent communication and synchronization of all model parameters (optimization variables) can be very…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space-time adaptive mesh refinement (AMR). The resulting…
In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a na\"{i}ve marking policy leads to inefficient use of computational resources for adaptive mesh refinement…