Related papers: Parallel Domain Decomposition techniques applied t…
Advances in high-performance computing require new ways to represent large-scale scientific data to support data storage, data transfers, and data analysis within scientific workflows. Multivariate functional approximation (MFA) has…
Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…
In the framework of Symbolic Data Analysis (SDA), distribution-variables are a particular case of multi-valued variables: each unit is represented by a set of distributions (e.g. histograms, density functions or quantile functions), one for…
Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…
With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational methods are required to take advantage of such extreme-scale machines. In this…
In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…
Mosaic Flow is a novel domain decomposition method designed to scale physics-informed neural PDE solvers to large domains. Its unique approach leverages pre-trained networks on small domains to solve partial differential equations on large…
We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The…
Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…
As time-series applications grow larger, there is increasing demand for symbolic representations that are compact, accurate, and scalable across many signals and computing resources. Current ABBA-based symbolic approximation methods produce…
When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at…
Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable…
Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary optimality system consists of one forward and one backward…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…