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Computational notebooks such as Jupyter are popular for exploratory data analysis and insight finding. Despite the module-based structure, notebooks visually appear as a single thread of interleaved cells containing text, code,…

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…

Accelerators such as neural processing units (NPUs) deliver an enticing balance of performance and efficiency compared to general purpose compute architectures. However, effectively leveraging accelerator capabilities is not always simple:…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…

The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…

Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…

Computing students increasingly rely on generative AI tools for programming assistance, often without formal instruction or guidance. This highlights a need to teach students how to effectively interact with AI models, particularly through…

We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…

In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the…

We consider an environmental interface regarding as a complex system, in which difference equations for calculating the environmental interface temperature and deeper soil layer temperature are represented by the coupled maps. First…

To harness the potential of advanced computing technologies, efficient (real time) analysis of large amounts of data is as essential as are front-line simulations. In order to optimise this process, experts need to be supported by…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…

Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…

In this paper, we introduce a new three-step iteration process in Banach space and prove convergence results for approximating fixed points for nonexpansive mappings. Also, we show that the newly introduced iteration process converges…

Segmenting objects of interest in an image is an essential building block of applications such as photo-editing and image analysis. Under interactive settings, one should achieve good segmentations while minimizing user input. Current deep…

We revisit the implementation of iterative solvers on discrete graphics processing units and demonstrate the benefit of implementations using extensive kernel fusion for pipelined formulations over conventional implementations of classical…