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We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…

Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related…

There is increasing demand for automated systems that can fabricate 3D structures. Robotic spatial extrusion has become an attractive alternative to traditional layer-based 3D printing due to a manipulator's flexibility to print large,…

An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and…

Spatial modeling of wireless networks via analytical means has been considered as a widely practiced mechanism for inference. As a result, some geometrical deployment models have been proposed in literature. Although practical in certain…

In this paper we study the use of Virtual Element method for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes that form the reservoirs, such as sedimentation, erosion and faulting, lead to…

In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…

For the design of gridshells consisting of continuous beams in two directions and quadrilateral faces to cover a large space of architecture, it is important to arrange each row and column of beams along a planar curve and ensure planar…

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with…

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…

Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…

We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…

Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…

This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…