Simulation of Wave Propagation
http://hdl.handle.net/20.500.11824/8
Sat, 26 Nov 2022 21:57:42 GMT2022-11-26T21:57:42ZZindler-type hypersurfaces in R^4
http://hdl.handle.net/20.500.11824/1519
Zindler-type hypersurfaces in R^4
Martinez-Maure, Y.; Rochera, D.
In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symplectic geometry are used. Moreover, each Zindler hypersurface is fibrated by space Zindler curves that correspond, in the convex case, to some space curves of constant width lying on the associated hypersurface of constant width and with the same symplectic area.
Thu, 08 Sep 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15192022-09-08T00:00:00ZThe DPG Method for the Convection-Reaction Problem, Revisited
http://hdl.handle.net/20.500.11824/1512
The DPG Method for the Convection-Reaction Problem, Revisited
Demkowicz, L.; Roberts, N.V.; Muñoz-Matute, J.
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin operator - is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15122022-01-01T00:00:00ZMachining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
http://hdl.handle.net/20.500.11824/1508
Machining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
Mishra, S.; Escudero, G.; Gonzalez, H.; Calleja, A.; Martinez, S.; Barton, M.; Lopez de Lacalle, N.; Mishra
The microstructure-supported design of engineering components is recently gaining attention due to their high strength-to-weight and high stiffness-to-weight properties. The present study investigates the hybrid manufacturing of Inconel 718 curved thin walls with internal microstructural supports fabricated by laser powder bed fusion (LPBF). Printed walls contain a fixed curvature and thickness, whereas the internal microstructures were varied at different inclination angles. In this research, a finish milling operation has been performed at different milling parameters. Machining-induced damages on the internal microstructures have been studied and correlated with geometrical deviation and surface integrity features on the outer thin wall surfaces.
Fri, 01 Jul 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15082022-07-01T00:00:00Z1D Painless Multi-level Automatic Goal-Oriented h and p Adaptive Strategies Using a Pseudo-Dual Operator
http://hdl.handle.net/20.500.11824/1507
1D Painless Multi-level Automatic Goal-Oriented h and p Adaptive Strategies Using a Pseudo-Dual Operator
Caro, F.V.; Darrigrand, V.; Alvarez-Aramberri, J.; Alberdi, E.; Pardo, D.
The main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are removed according to their estimated importance. Many Goal-Oriented Adaptive strategies represent the error in a Quantity of Interest (QoI) in terms of the bilinear form and the solution of the direct and adjoint problems. However, this is unfeasible when solving indefinite or non-symmetric problems since symmetric and positive definite forms are needed to define the inner product that guides the refinements. In this work, we provide a Goal-Oriented Adaptive (h- or p-) strategy whose error in the QoI is represented in another bilinear symmetric positive definite form than the one given by the adjoint problem. For that purpose, our Finite Element implementation employs a multi-level hierarchical data structure that imposes Dirichlet homogeneous nodes to avoid the so-called hanging nodes. We illustrate the convergence of the proposed approach for 1D Helmholtz and convection-dominated problems.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/15072022-01-01T00:00:00Z