A5007929651- Advanced Numerical Methods in Computational Mathematics
- Computational Fluid Dynamics and Aerodynamics
- Advanced Mathematical Modeling in Engineering
- Numerical methods for differential equations
- Fluid Dynamics and Turbulent Flows
- Electromagnetic Simulation and Numerical Methods
- Numerical methods in engineering
- Meteorological Phenomena and Simulations
- Lattice Boltzmann Simulation Studies
- Distributed and Parallel Computing Systems
- Differential Equations and Numerical Methods
- Model Reduction and Neural Networks
- Gas Dynamics and Kinetic Theory
- Parallel Computing and Optimization Techniques
- Matrix Theory and Algorithms
- Advanced Numerical Analysis Techniques
- Numerical methods in inverse problems
- Solar and Space Plasma Dynamics
- Computer Graphics and Visualization Techniques
- Hydrology and Watershed Management Studies
- Computational Geometry and Mesh Generation
- Magnetic confinement fusion research
- Flood Risk Assessment and Management
- Peer-to-Peer Network Technologies
- Scientific Computing and Data Management
University of Warwick
2014-2024
Politecnico di Milano
2015
University of Freiburg
2002-2012
This paper presents the basic concepts and module structure of Distributed Unified Numerics Environment reflects on recent developments general changes that happened since release first Dune version in 2007 main papers describing state Bastian etal. (2008a, 2008b). discussion is accompanied with a description various advanced features, such as coupling domains cut cells, grid modifications adaptation moving domains, high order discretizations node level performance, non-smooth multigrid...
The Dune project has released version 2.4 on September 25, 2015. This paper describes the most significant improvements, interface and other changes for core modules Dune- Common, Dune-Geometry, Dune-Grid, Dune-ISTL, Dune-LocalFunctions.
Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and resulting surface voltages measured. It has potential distinguish between ischaemic haemorrhagic stroke with portable inexpensive device. The image reconstruction relies on an accurate forward model of experimental setup. Because relatively small signal in EIT, finite-element modeling requires meshes more than 10 million elements. To study requirements EIT also...
We extend the discontinuous Galerkin framework to a linear second-order elliptic problem on compact smooth connected and oriented surface in ℝ3. An interior penalty (IP) method is introduced discrete we derive priori error estimates by relating latter original via lift Dziuk (1988). The suggest that geometric terms arising from discretization do not affect overall convergence rate of IP when using ansatz functions. This then verified numerically for number test problems. intricate issue...
We derive and analyze high order discontinuous Galerkin methods for second elliptic problems on implicitly defined surfaces in $\mathbb{R}^{3}$. This is done by carefully adapting the unified framework of [D. N. Arnold et al., SIAM J. Numer. Anal., 39 (2002), pp. 1749--1779] a triangulated surface approximating smooth surface. prove optimal error estimates both (mesh dependent) energy $L^2$ norms. Numerical results validating our theoretical are also presented.
In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of sources from ALUGrid library and binding to DUNE software framework. The main improvements concern parallel feature set library. changes include user-defined load balancing, grid construction, an redesign 2d which can now also be used for computations. addition many have been introduced into code increase efficiency decrease memory footprint. original is widely within community due its good...
.In this paper we present a framework for the construction and implementation of general virtual element spaces based on projections built from constrained least squares problems. Building triples used finite spaces, introduce concept method (VEM) tuple which encodes necessary building blocks to construct these projections. Using approach, wide range can be defined. We discuss \(H^k\)-conforming \(k=1,2\) as well divergence curl free spaces. This has advantage being easily integrated into...
We present a new scheme, the compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with detailed comparison to other well-accepted DG methods. The CDG2 method is similar CDG that was recently introduced in work of Perraire and Persson elliptic problems. One main feature compactness stencil which includes only neighboring elements, even higher order approximation. Theoretical results showing coercivity stability Poisson heat equation are...
We consider an elliptic optimal control problem where the objective functional contains evaluations of state at a finite number points. In particular, we use fidelity term that encourages to take certain values these points, which means our is related ones with constraints The analysis and numerical differs from when in |$L^2$|-norm because need space embed into continuous functions. this paper, discretize using two different piecewise linear element methods. For each discretization...
We propose an a posteriori error estimate for the Runge–Kutta discontinuous Galerkin method (RK‐DG) of arbitrary order in space dimensions. For stabilization scheme general framework projections is introduced. Finally it demonstrated numerically how used to design both efficient grid adaption and gradient limiting strategy. Numerical experiments show stability gain efficiency comparison with computations on uniform grids.
We present a class of nonconforming virtual element methods for general fourth-order partial differential equations in two dimensions. develop generic approach constructing the necessary projection operators and spaces. Optimal error estimates energy norm are provided linear problems with varying coefficients. also discuss perturbation novel scheme which is uniformly convergent respect to parameter without requiring an enlargement space. Numerical tests carried out verify theoretical...