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In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified N\'ed\'elec-Raviart-Thomas finite element methods for model problems in $\mathbf{H}(\operatorname{\mathbf{curl}})$ and…
We present a high-level domain-specific language (DSL) interface to drive an adaptive incomplete $k$-d tree-based framework for finite element (FEM) solutions to PDEs. This DSL provides three key advances: (a) it abstracts out the…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Current quantum programming is dominated by low-level, circuit-centric approaches that limit the potential for compiler optimization. This work presents how a high-level programming construct provides compilers with the semantic information…
Optimization of large structures of multiple components is essential to many industries for minimizing mass, especially the design of aerospace vehicles. Optimizing a single primary load member independently of all other primary structures…
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 paper presents an analysis of the energy consumption of an extensive number of the optimisations a modern compiler can perform. Using GCC as a test case, we evaluate a set of ten carefully selected benchmarks for five different…
While implicit Runge--Kutta methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebraic system at each time step are frequently cited as…
Energy efficiency has a significant influence on user experience of battery-driven devices such as smartphones and tablets. The goal of an energy model for source code is to lay a foundation for the application of energy-saving techniques…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…
FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
Open Answer Set Programming (OASP) is an attractive framework for integrating ontologies and rules. In general OASP is undecidable. In previous work we provided a tableau-based algorithm for satisfiability checking w.r.t. forest logic…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
In the rapidly evolving industry of software development, coding efficiency and accuracy play significant roles in delivering high-quality software. Various code suggestion and completion tools, such as CodeBERT from Microsoft and GPT-3.5…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the…