相关论文: $\varphi$enics: Vainshtein screening with the fini…
The present manuscript presents a framework for automating the formulation and resolution of limit analysis problems in a very general manner. This framework relies on FEniCS domain-specific language and the representation of material…
In this part, we apply the same finite-element approach, used in Part III for the vanishing first traveltime variation (to obtain the stationary rays), for the second traveltime variation, in order to compute the dynamic characteristics…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
This paper develops a renormalized perturbation theory framework for nonlinear structure formation in a broad class of modified gravity models that exhibit Vainshtein screening, with a focus on a viable subclass of Horndeski theories. We…
We investigate the efficiency of screening mechanisms in the hybrid metric-Palatini gravity. The value of the field is computed around spherical bodies embedded in a background of constant density. We find a thin shell condition for the…
A screening mechanism for conformal vector-tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
We study static spherically symmetric solutions of massive bi-gravity theory, free from the Boulware-Deser ghost. We show the recovery of General Relativity via the Vainshtein mechanism, in the weak limit of the physical metric. We find a…
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence)…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
In this PhD thesis I make use of the "Effective Field Theory of Gravity for Extended Objects" by Goldberger and Rothstein in order to investigate theories of gravity and to take a different point of view on the physical information that can…
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…