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The Stokes-Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate…
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…
This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms. Applicability of these methods to large scale inverse problems is however limited by the available memory for…
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…
Existing self-supervised monocular depth estimation methods can get rid of expensive annotations and achieve promising results. However, these methods suffer from severe performance degradation when directly adopting a model trained on a…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…
The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…
We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids. The grid layout we consider consists of a nested hierarchy of fixed size,…
We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been…
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
Motivated by a wide range of real-world problems whose solutions exhibit boundary and interior layers, the numerical analysis of discretizations of singularly perturbed differential equations is an established sub-discipline within the…
As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…