Related papers: Adaptive Multigrid Strategy for Geometry Optimizat…
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…
Microfluidic devices are gaining attention for their small size and ability to handle tiny fluid volumes. Mixing fluids efficiently at this scale, known as micromixing, is crucial. This article builds upon previous research by introducing a…
A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are…
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…
We present GridFF, an efficient method for simulating molecules on rigid substrates, derived from techniques used in protein-ligand docking in biochemistry. By projecting molecule-substrate interactions onto precomputed spatial grids with…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
Low order, sequential or non-massively parallel finite elements are generaly used for three-dimensional gravity modelling. In this paper, in order to obtain better gravity anomaly solutions in heterogeneous media, we solve the gravimetry…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
We develop a general distributed implementation of an adaptive fast multipole method in three space dimensions. We rely on a balanced type of adaptive space discretisation which supports a highly transparent and fully distributed…
Fully adaptive computations of the resistive magnetohydrodynamic (MHD) equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control…
Atomistic/continuum coupling method is a class of multiscale computational method for the efficient simulation of crystalline defects. The recently developed blended ghost force correction (BGFC) method combines the efficiency of blending…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
The paper investigates the complex gradient descent method (CGD) for the best rational approximation of a given order to a function in the Hardy space on the unit disk. It is equivalent to finding the best Blaschke form with free poles. The…
Rapid advancements in machine learning (ML) are transforming materials science by significantly speeding up material property calculations. However, the proliferation of ML approaches has made it challenging for scientists to keep up with…
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…
We advertise the use of tetrahedral grids constructed via the longest edge bisection algorithm for rendering volumetric data with path tracing. The key benefits of such grids is two-fold. First, they provide a highly adaptive…