Related papers: The Minimal Geometric Deformation Approach: a brie…
A kinematical description of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…
The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the GDM to establish a first general error estimate for numerical…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
We present a hybrid method combining a minimizing movement scheme with neural operators for the simulation of phase field-based Willmore flow. The minimizing movement component is based on a standard optimization problem on a regular grid…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
The characteristic decomposition for GRMHD is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we…
Generalized Lambda-semiflows are an abstraction of semiflows with non-periodic solutions, for which there may be more than one solution corresponding to given initial data. A select class of solutions to generalized Lambda-semiflows is…
We present a new approach to rigid-body motion segmentation from two views. We use a previously developed nonlinear embedding of two-view point correspondences into a 9-dimensional space and identify the different motions by segmenting…
In this work, we investigate wormhole solutions through the utilization of gravitational decoupling, employing the Minimal Geometric Deformation (MGD) procedure within the framework of Trace-Free Gravity. We base our investigation on static…
Computational modeling of the brain has become a key part of understanding how the brain clears metabolic waste, but patient-specific modeling on a significant scale is still out of reach with current methods. We introduce a novel approach…
A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the later is…
We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as well as open hypersurfaces with moving contact lines in three…
The question of interest in the present study is: ``Given a body subject to mechanical loads, how to define the initial geometry so that the deformed one matches precisely a prescribed shape?'' This question is particularly relevant in…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
We develop a gauge-invariant formalism to describe metric perturbations in five-dimensional brane-world theories. In particular, this formalism applies to models originating from heterotic M-theory. We introduce a generalized longitudinal…
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…