Related papers: A Global Method for Relaxation for Multi-levelled …
The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours,…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a…
With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution.…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…
A computational approach is presented to obtain energy-minimized structures in glassy materials. This approach, the activation-relaxation technique (ART), achieves its efficiency by focusing on significant changes in the microscopic…
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there…
Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which…
How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of…
The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first present the functional framework on the example of a linear…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…
This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…