Related papers: High-Order Finite-differences on multi-threaded ar…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
Multi-objective integer optimization problems are hard to solve, mainly because the number of nondominated images is often extremely large. We present the first exact algorithm, called PEA, that fully utilizes the multicore architecture of…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
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…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
In this paper, we propose a methodology for partitioning and mapping computational intensive applications in reconfigurable hardware blocks of different granularity. A generic hybrid reconfigurable architecture is considered so as the…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
An increasingly large number of HPC systems rely on heterogeneous architectures combining traditional multi-core CPUs with power efficient accelerators. Designing efficient applications for these systems has been troublesome in the past as…