Documents published in Scipedia

• Adaptive Finite Elements With large aspect ratio for Aluminium Electrolysis

  P. Passelli, M. Picasso

  admos2023.

  
  

  Abstract

  A continuation anisotropic adaptive algorithm to solve elliptic PDEs is pre sented. The p-laplacian problem and the Stokes equation are considered. The algorithm is based on an a posteriori error indicator justified in [7] and [10]. The goal is to produce an anisotropic mesh such that the relative estimated error is close to a preset tolerance TOL. A continuation method is used to decrease TOL. Numerical results show that the computational time is considerably reduced when using such a continuation algorithm.

  Abstract
  A continuation anisotropic adaptive algorithm to solve elliptic PDEs is pre sented. The p-laplacian problem and the Stokes equation are considered. The algorithm is based [...]

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• DynAMO: Dynamic Anticipatory Mesh Optimization for Hyperbolic PDEs using Reinforcement Learning

  K. Mittal, T. Dzanic, J. Yang, S. Petrides, D. Kim, B. Keith, A. Gillette, R. Anderson, D. Faissol

  admos2023.

  
  

  • 4
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• On the Use of Neural Networks for Inverse Problems

  L. Herrmann, T. Bürchner, S. Kollmannsberger

  admos2023.

  
  

  • 4
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• SuperAdjoint: Super-Resolution Neural Networks in Adjoint-based Output Error Estimation

  T. Hunter, S. Hulsoff, A. Sitaram

  admos2023.

  
  

  Abstract

  Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Adjoint-based error estimation is the most accurate method, and generally the most costly. A strong contributor to this cost is the need to compute a higher resolution adjoint solution, using time dependent information. Here, recontruction methods applied to the primal and adjoint solutions are proposed to alleviate both the storage footprint of the primal problem and the adjoint computational cost. The method is compared to reference error estimators on an unsteady Burgers’ equation using the method of manufactured solutions. Two reconstruction methods, a proper orthogonal decomposition and a static convolutional neural network were used to demonstrate both the computational cost reduction and the potential for the reduction of the storage footprint of the primal problem. When reconstruction methods are applied to the primal problem, one can use both proposed approaches to reduce the footprint of the solution and reconstruct the effectively compressed primal solution to be recalled for the adjoint solution. The second approach consists in solving an adjoint solution from a coarse primal solution and using reconstruction methods to obtain a higher resolution adjoint solution, necessary for output error estimation and mesh adaptation. The obtained results give great confidence in the use of reconstruction methods for the reduction of both computational cost and storage requirements of adjoint-based error estimation, and goal-oriented mesh adaptation.

  Abstract
  Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Adjoint-based error estimation [...]

  • 2
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• A hybrid adaptive method for initial-boundary value problems

  K. Mattsson, G. Eriksson, V. Stiernström, T. Ahn Dao

  admos2023.

  
  

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• Error Estimation for the Material Point and Particle in Cell Methods

  M. Berzins

  admos2023.

  
  

  Abstract

  The Material Point Method (MPM) is widely used for challenging applica tions in engineering, and animation. The complexity of the method makes error estimation challenging. Error analysis of a simple MPM method is undertaken and the global error is shown to be first order in space and time for a widely-used variant of the method. Computational experiments illustrate the estimated accuracy.

  Abstract
  The Material Point Method (MPM) is widely used for challenging applica tions in engineering, and animation. The complexity of the method makes error estimation challenging. [...]

  • 22
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• Real-time monitoring of additive manufacturing processes using a variational data assimilation method with model reduction and bias correction

  L. Chamoin, W. Haik, Y. Maday

  admos2023.

  
  

  • 4
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• Algal Cultivation for Bioenergy Production: First Mathematical Modelling Results in Raceways

  A. Martínez, L. Alvarez-Vázquez, C. Rodríguez, M. Vázquez-Méndez

  admos2023.

  
  

  Abstract

  The most used algae cultivation systems are the open-channel raceway ponds for their low maintenance and energy costs. Raceways allow algal cultivation using wastewater, where algae mass can be employed as source for bioenergy production. One of the main external factors influencing algal productivity is the velocity of the liquid inside the pond, that can be easily controlled by the position and/or rotational speed of the turning paddle wheel, and by the height of water. In this work we introduce a novel methodology to automate the optimization of the design of raceway ponds based on techniques of optimal control of partial differential equations. So, we formulate the problem as a control problem where the state system is given by the coupled nonlinear equations for hydrodynamics and algae/nitrogen/phosphorus concentrations, and the objective function to be maximized represents the global concentration of algae at final time. We present here a detailed, rigorous mathematical formulation of the optimal control problem, we propose a numerical algorithm for its resolution, and we show some preliminary computational results related to the numerical modelling of the problem.

  Abstract
  The most used algae cultivation systems are the open-channel raceway ponds for their low maintenance and energy costs. Raceways allow algal cultivation using wastewater, where [...]

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• Towards a More Efficient Evacuation of Crowds by Means of an Optimal Location of Exit Doors

  L. Alvarez-Vázquez, N. García-Chan, A. Martínez, C. Rodríguez, M. Vázquez-Méndez

  admos2023.

  
  

  Abstract

  In this work we present a new strategy, employing optimal control techniques of partial differential equations, to automate the optimization of locations for a given number of exit doors at gathering places, so that the evacuation of crowds takes place in a safer and faster way. Once given a detailed mathematical formulation of the problem, in order to solve the constrained optimal control problem numerically, we propose its full discretization, with a space semi-discretization via the finite element method over a family of triangular meshes of the domain under study, and a time semi-discretization via the Euler algorithm. Finally, for the resulting discretized minimization problem, we try its optimization by means of a derivative-free algorithm. Numerical examples, corresponding to different scenarios for a real-world study case posed on “Plaza de la Liberación” (Guadalajara, Mexico), are presented and discussed to assess the effectiveness of our approach.

  Abstract
  In this work we present a new strategy, employing optimal control techniques of partial differential equations, to automate the optimization of locations for a given number [...]

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• Accelerating model order reduction by multi-fidelity error estimation

  L. Feng, L. Lombardi, G. Antonini, P. Benner

  admos2023.

  
  

  • 4
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