相关论文: ParMooN - a modernized program package based on ma…

Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…

Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which…

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…

The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…

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…

We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…

With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…

A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle…

Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set…

The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…

Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar…

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…

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…

Python has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related…

We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…

Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the…