Related papers: R-Adaptive Mesh Optimization to Enhance Finite Ele…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
Today's scientific simulations generate exceptionally large volumes of data, challenging the capacities of available I/O bandwidth and storage space. This necessitates a substantial reduction in data volume, for which error-bounded lossy…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
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 review some recent work on the enhancement and application of both r- and h- adaptation techniques, benefitting of the functionalities of the remeshing platform Mmg: www.mmgtools.org. Several contributions revolve around the level-set…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
Designing efficient optimizers for large language models (LLMs) with low-memory requirements and fast convergence is an important and challenging problem. This paper makes a step towards the systematic design of such optimizers through the…
Accurate simulations of various physical processes on digital computers requires huge computing performance, therefore accelerating these scientific and engineering applications has a great importance. Density of programmable logic devices…
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
The internal structure and operation mechanism of large-scale language models are analyzed theoretically, especially how Transformer and its derivative architectures can restrict computing efficiency while capturing long-term dependencies.…
Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…
Computing has a huge memory problem. The memory system, consisting of multiple technologies at different levels, is responsible for most of the energy consumption, performance bottlenecks, robustness problems, monetary cost, and hardware…
Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…
Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical model-based reconstructions (termed physics-based…
In today's uncertain and competitive market, where enterprises are subjected to increasingly shortened product life-cycles and frequent volume changes, reconfigurable manufacturing systems (RMS) applications play a significant role in the…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
This paper describes a memory-efficient transformer model designed to drive a reduction in memory usage and execution time by substantial orders of magnitude without impairing the model's performance near that of the original model.…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…