Related papers: Efficient Numerical Integration for Finite Element…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Harmonic inpainting with optimised data is very popular for inpainting-based image compression. We improve this approach in three important aspects. Firstly, we replace the standard finite differences discretisation by a finite element…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form…
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
Early stopping techniques can be utilized to decrease the time cost, however currently the ultimate goal of early stopping techniques is closely related to the accuracy upgrade or the ability of the neural network to generalize better on…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
Quantization of weights and activations in Deep Neural Networks (DNNs) is a powerful technique for network compression, and has enjoyed significant attention and success. However, much of the inference-time benefit of quantization is…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated…