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The gravitation theory is modified on the base of geometric identity and equivalence principle. This makes it possible to generalize the geodesics and solve several problems of classical GRT such as flat rotation curves of the spiral…
The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological $N$-body simulations…
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…
Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of…
There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
We present the geodesics on homogeneous and isotropic negatively curved spaces in a simple form suitable for application to cosmological problems. We discuss how the patterns in the microwave sky of anisotropic homogeneous universes can be…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
Inhomogeneous and anisotropic cosmologies are modeled withing the framework of scalar-tensor gravity theories. The inhomogeneities are calculated to third-order in the so-called long-wavelength iteration scheme. We write the solutions for…
A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
We solve the equations of topologically massive gravity with potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations,…
The present work represents a step to deal with stellar structure using a pure geometric approach. A geometric field theory is used to construct a model for a spherically symmetric configuration. The model obtained can be considered as a…
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
High-dimensional visual computer models are poised to revolutionize the space mission design process. The circular restricted three-body problem (CR3BP) gives rise to high-dimensional toroidal manifolds that are of immense interest to…
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion…
We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex…