Related papers: Acoustic shape optimization using energy stable cu…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of…
The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and…
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…
Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability, or bring forward a bifurcation to enable rapid switching between states.…
In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…