arXiv subjects

Dirk Roose

Publications and source records attributed to Dirk Roose.

9 recordsLinked to original sources

arXiv2022

Selecting cells in a raster database for maximal impact intervention in the presence of spatial interaction: Computational complexity of a Multiple vs. a Single Flow Direction Method

To minimize the sediment flowing to the outlet of a river catchment with minimal effort or cost, it is important to select the best areas to perform a certain intervention, e.g., afforestation. CAMF (Cellular Automata based heuristic for Minimizing Flow) is a method that performs this selection process iteratively in a raster geodatabase environment. To simulate the flow paths, the original CAMF uses a Single Flow Direction (SFD) algorithm. However, SFD fails to reflect the real nature of flow transport, especially in areas with low relief. This paper describes and analyzes the integration of a Multiple Flow Direction (MFD) algorithm in CAMF, in order to provide a more realistic flow simulation. We compare the computational complexity of CAMF-SFD and CAMF-MFD and we discuss the scalability w.r.t. the number of cells involved. We evaluate the behavior of both variants for sediment yield minimization by afforestation in two catchments with different properties.

cs.CE↗

arXiv2021

Parameter Tuning Strategies for Metaheuristic Methods Applied to Discrete Optimization of Structural Design

This paper presents several strategies to tune the parameters of metaheuristic methods for (discrete) design optimization of reinforced concrete (RC) structures. A novel utility metric is proposed, based on the area under the average performance curve. The process of modelling, analysis and design of realistic RC structures leads to objective functions for which the evaluation is computationally very expensive. To avoid costly simulations, two types of surrogate models are used. The first one consists of the creation of a database containing all possible solutions. The second one uses benchmark functions to create a discrete sub-space of them, simulating the main features of realistic problems. Parameter tuning of four metaheuristics is performed based on two strategies. The main difference between them is the parameter control established to perform partial assessments. The simplest strategy is suitable to tune good `generalist' methods, i.e., methods with good performance regardless the parameter configuration. The other one is more expensive, but is well suited to assess any method. Tuning results prove that Biogeography-Based Optimization, a relatively new evolutionary algorithm, outperforms other methods such as GA or PSO for such optimization problems, due to its particular approach of applying recombination and mutation operators.

cs.NE↗

arXiv2021

A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation

We present a fast algorithm to solve nesting problems based on a semi-discrete representation of both the 2D non-convex pieces and the strip. The pieces and the strip are represented by a set of equidistant vertical line segments. The discretization algorithm uses a sweep-line method and applies minimal extensions to the line segments of a piece to ensure that non-overlapping placement of the segments, representing two pieces, cannot cause overlap of the original pieces. We implemented a bottom-left-fill greedy placement procedure, using an optimised ordering of the segments overlap tests. The C++ implementation of our algorithm uses appropriate data structures that allow fast execution. It executes the bottom-left-fill algorithm for typical ESICUP data sets in a few milliseconds, even when rotation of the pieces is considered, and thus provides a suitable `building block' for integration in metaheuristics. Moreover, we show that the algorithm scales well when the number of pieces increases.

cs.CG↗

arXiv2016

DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations

DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with discrete constant and state-dependent delays. The package supports continuation and stability analysis of steady state solutions and periodic solutions. Further one can compute and continue several local and global bifurcations: fold and Hopf bifurcations of steady states; folds, period doublings and torus bifurcations of periodic orbits; and connecting orbits between equilibria. To analyse the stability of steady state solutions, approximations are computed to the rightmost, stability-determining roots of the characteristic equation which can subsequently be used as starting values in a Newton procedure. For periodic solutions, approximations to the Floquet multipliers are computed. The manual describes the structure of the package, its routines, and its data and method parameter structures.

math.DS↗

arXiv2010

An approach for both the computation of coarse-scale steady state solutions and initialization on a slow manifold

We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain problems encountered by comparable existing approaches, and illustrate its use by computing coarse-scale steady states of a lattice Boltzmann fine scale code. Interestingly, in the same context of multiple time scale problems, the approach can be slightly modified to provide initial conditions (on the slow manifold) with prescribed coarse-scale observables. The approach is based on appropriately designed short bursts of the fine-scale simulator whose results are used to track changes in the coarse variables of interest, a core component of the equation-free framework.

physics.comp-ph↗

arXiv2006

Coarse-grained computation of traveling waves of lattice Boltzmann models with Newton-Krylov solvers

For many complex dynamical systems, a separation of scales prevails between the (microscopic) level of description of the available model, and the (macroscopic) level at which one would like to observe and analyze the system. For this type of problems, an ``equation-free'' framework has recently been proposed. Using appropriately initialized microscopic simulations, one can build a coarse-grained time-stepper to approximate a time-stepper for the unavailable macroscopic model. Here, we show how one can use this coarse-grained time-stepper to compute coarse-grained traveling wave solutions of a lattice Boltzmann model. In a moving frame, emulated by performing a shift-back operation after the coarse-grained time-step, the traveling wave appears as a steady state, which is computed using an iterative method, such as Newton--GMRES. To accelerate convergence of the GMRES procedure, a macroscopic model-based preconditioner is used, which is derived from the lattice Boltzmann model using a Chapman--Enskog expansion. We illustrate the approach on a lattice Boltzmann model for the Fisher equation and on a model for ionization waves.

physics.comp-ph↗

arXiv2004

Patch dynamics with buffers for homogenization problems

An important class of problems exhibits smooth behaviour on macroscopic space and time scales, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an "equation-free" framework has been proposed, of which patch dynamics is an essential component. Patch dynamics is designed to perform numerical simulations of an unavailable macroscopic equation on macroscopic time and length scales; it uses appropriately initialized simulations of the available microscopic model in a number of small boxes (patches), which cover only a fraction of the space-time domain. To reduce the effect of the artificially introduced box boundaries, we use buffer regions to "shield" the boundary artefacts from the interior of the domain for short time intervals. We analyze the accuracy of this scheme for a diffusion homogenization problem with periodic heterogeneity, and propose a simple heuristic to determine a sufficient buffer size. The algorithm performance is illustrated through a set of numerical examples, which include a non-linear reaction-diffusion equation and the Kuramoto--Sivashinsky equation.

physics.comp-ph↗

arXiv2003

The gap-tooth scheme for homogenization problems

An important class of problems exhibits smooth behaviour in space and time on a macroscopic scale, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an ``equation-free framework'' has been proposed, of which the gap-tooth scheme is an essential component. The gap-tooth scheme is designed to approximate a time-stepper for an unavailable macroscopic equation in a macroscopic domain; it uses appropriately initialized simulations of the available microscopic model in a number of small boxes, which cover only a fraction of the domain. We analyze the convergence of this scheme for a parabolic homogenization problem with non-linear reaction. In this case, the microscopic model is a partial differential equation with rapidly oscillating coefficients, while the unknown macroscopic model is approximated by the homogenized equation. We show that our method approximates a finite difference scheme of arbitrary (even) order for the homogenized equation when we appropriately constrain the microscopic problem in the boxes. We illustrate this theoretical result with numerical tests on several model problems. We also demonstrate that it is possible to obtain a convergent scheme without constraining the microscopic code, by introducing buffer regions around the computational boxes.

physics.comp-ph↗

arXiv2003

Damping factors for the gap-tooth scheme

An important class of problems exhibits macroscopically smooth behaviour in space and time, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, the gap-tooth scheme has recently been proposed. The scheme approximates the evolution of an unavailable (in closed form) macroscopic equation in a macroscopic domain; it only uses appropriately initialized simulations of the available microscopic model in a number of small boxes. For some model problems, including numerical homogenization, the scheme is essentially equivalent to a finite difference scheme, provided we repeatedly impose appropriate algebraic constraints on the solution for each box. Here, we demonstrate that it is possible to obtain a convergent scheme without constraining the microscopic code, by introducing buffers that "shield" over relatively short times the dynamics inside each box from boundary effects. We explore and quantify the behavior of these schemes systematically through the numerical computation of damping factors of the corresponding coarse time-stepper, for which no closed formula is available.

physics.comp-ph↗