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A Review of a B-spline based Volumetric Representation: Design, Analysis and Fabrication of Porous and/or Heterogeneous Geometries
Get PDFThe needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by geometric modeling tools that are based on boundary representations (B-reps) - AM requires the representation and manipulation of interior heterogeneous fields and materials. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) was conceived, contemporary GM systems only offer a loose link between the two, if at all.
For more than half a century, the (trimmed) Non-Uniform Rational B-spline (NURBs) surface representation has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this work, we review almost a decade of research and development in extending this boundary representation to a B-spline based, volumetric representation (V-rep) that successfully confronts the existing and anticipated design, analysis, and manufacturing foreseen challenges. We have extended all fundamental B-rep GM operations, such as primitive and surface constructors, and Boolean operations, to trimmed trivariate V-reps. This enables the much-needed tight link between the designed geometry and (iso-geometric) analysis on one hand and the full support of (additive) manufacturing of porous, (graded-) heterogeneous and anisotropic geometries, on the other. Examples and applications of V-rep GM, that span design, analysis and optimization, and AM, of lattice- and micro-structure synthesis as well as graded-heterogeneity, are demonstrated, with emphasis on AM
Local wind speed forecasting based on WRF-HDWind coupling
Get PDFWind speed forecasts obtained by Numerical Weather Prediction models are limited for fine interpretation in heterogeneous terrain, in which different roughnesses and orographies occur. This limitation is derived from the use of low-resolution and grid-box averaged data. In this paper a dynamical downscaling method is presented to increase the local accuracy of wind speed forecasts. The proposed method divides the wind speed forecasting into two steps. In the first one, the mesoscale model WRF (Weather Research and Forecasting) is used for getting wind speed forecasts at specific points of the study domain. On a second stage, these values are used for feeding the HDWind microscale model. HDWind is a local model that provides both a high-resolution wind field that covers the entire study domain and values of wind speed and direction at very located points. As an example of use of the proposed method, we calculate a high-resolution wind field in an urban-interface area from Badajoz, a South-West Spanish city located near the Portugal border. The results obtained are compared with the values read by a weathervane tower of the Spanish State Meteorological Agency (AEMET) in order to prove that the microscale model improves the forecasts obtained by the mesoscale model
SOLUTIONS TO THE NONLINEAR OBSTACLE PROBLEM WITH COMPACT CONTACT SETS
No full textFor the obstacle problem with a nonlinear operator, we character-
ize the space of global solutions with compact contact sets. This is achieved
by constructing a bijection onto a class of quadratic polynomials describing
the asymptotic behavior of solutions
From the free energy principle to a confederation of Bayesian mechanics: Reply to comments on “How particular is the physics of the free energy principle?”
No full textThe Natural Bias of Artificial Instances
Get PDFMany exact and metaheuristic algorithms presented in the literature are tested by comparing their performance in different sets of instances. However, it is known that when these sets of instances are generated randomly, they neither have nor fulfill the features the authors believe they do, which implies that wrong conclusions were made. In this paper, we reinforce the importance of analyzing randomly generated instances by sampling the problem coefficients uniformly at random. We generate instances of the Unconstrained Binary Quadratic Problem and the Number Partitioning Problem. In both cases, we verify that the generated set of instances do not represent a uniform set of instances of the problem. We have conducted several experiments to quantify the number of different rankings of solutions that the problems can generate. We have classified those rankings according to how often each ranking is sampled, how many local optimal solutions each ranking has, and how similar they are.PID2019-104966GB-I00,
PID2019-104933GB-I00,
PID2019-106453GA-I00 funded by MCIN/AEI/10.13039/501100011033,
Basque Government through the program BERC 2022–2025, IT1504-22 and IT1494-22;
UPV/EHU through GIU20/054.
PRE_2021_2_022
Mellin definition of the fractional Laplacian
Get PDFIt is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is applied to radial functions. The main finding is tested in the case of the space-fractional diffusion equation. The one-dimensional case is also considered, such that the Mellin transform of the Riesz (namely the symmetric Riesz–Feller) fractional derivative is established. This one-dimensional result corrects an existing formula in literature. Further results for the Riesz fractional derivative are obtained when it is applied to symmetric functions, in particular its relation with the Caputo and the Riemann– Liouville fractional derivatives.CEX2021-001142-S / MICIN / AEI / 10.13039/50110001103
MONITORING MOORING (MONIMOOR) LINES OF FLOATING STRUCTURES USING DEEP LEARNING-BASED APPROACHES
No full textShape Optimization for Temperature Regulation in Extrusion Dies Using Microstructures
Get PDFPlastic profile extrusion—a manufacturing process for continuous profiles with fixed cross section—requires a complex and iterative design process to prevent deformations and residual stresses in the final product. The central task is to ensure a uniform material velocity at the outlet. To this end, not only the geometry of the flow decisively influences the quality of the outflow but also the temperature profile along the flow channel wall. It is exactly here that this work contributes by presenting a novel design approach for extrusion dies that will allow for optimal temperature profiles. The core of this approach is the composition of the extrusion die through microstructures. The optimal shape and distribution of these microstructures is determined via shape optimization. The corresponding optimization procedure is the main topic of this article. Special emphasis is placed on the definition of a suitable, low-dimensional shape parameterization. The proposed design-framework is then applied to two numerical test cases with varying complexity
Qualitative Numerical Analysis of a Free-Boundary Diffusive Logistic Model
Get PDFA two-dimensional free-boundary diffusive logistic model with radial symmetry is consid- ered. This model is used in various fields to describe the dynamics of spreading in different media: fire propagation, spreading of population or biological invasions. Due to the radial symmetry, the free boundary can be treated by a front-fixing approach resulting in a fixed-domain non-linear problem, which is solved by an explicit finite difference method. Qualitative numerical analysis establishes the stability, positivity and monotonicity conditions. Special attention is paid to the spreading–vanishing dichotomy and a numerical algorithm for the spreading–vanishing boundary is proposed. Theoretical statements are illustrated by numerical tests
An Historical Review of the Simplified Physical Fire Spread Model PhyFire: Model and Numerical Methods
Get PDFA historical review is conducted of PhyFire, a simplified physical forest fire spread model developed by the research group on Numerical Simulation and Scientific Computation (SINUMCC) at the University of Salamanca. The review ranges from the first version of the model to the current one now integrated into GIS, considering all the mathematical problems and numerical methods involved throughout its development: finite differences, mixed, classical and adaptive finite elements, data assimilation, sensitivity analysis, parameter adjustment, and parallel computation, among others. The simulation of processes as complex as forest fires involves a multidisciplinary effort that is constantly being enhanced, while posing interesting challenges from a mathematical, numerical, and computational perspective, without losing sight of the overriding aim of developing an efficient, effective, and useful simulation tool