Related papers: Massively parallel-in-space-time, adaptive finite …
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes.…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
The idle computers on a local area, campus area, or even wide area network represent a significant computational resource---one that is, however, also unreliable, heterogeneous, and opportunistic. This type of resource has been used…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and…
Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…
A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
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…
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable…