Computational Mathematics (CM)http://hdl.handle.net/20.500.11824/52021-09-17T02:17:30Z2021-09-17T02:17:30ZDeep learning driven self-adaptive hp finite element methodPaszyński, M.Grzeszczuk, R.Pardo, D.Demkowicz, L.http://hdl.handle.net/20.500.11824/13352021-09-15T01:00:31Z2021-06-01T00:00:00ZDeep learning driven self-adaptive hp finite element method
Paszyński, M.; Grzeszczuk, R.; Pardo, D.; Demkowicz, L.
The fi nite element method (FEM) is a popular tool for solving engineering problems governed by Partial Di fferential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational mesh. We consider the self-adaptive hp-FEM, which generates optimal mesh refi nements and delivers exponential convergence of the numerical error with respect to the mesh size. Thus, it enables solving di ficult engineering problems with the highest possible numerical accuracy. We replace the computationally expensive kernel of the refi nement algorithm with a deep neural network in this work. The network learns how to optimally re fine the elements and modify the orders of the polynomials. In this way, the deterministic algorithm is replaced
by a neural network that selects similar quality refi nements in a fraction of the time needed by the original algorithm.
2021-06-01T00:00:00ZLarge-offset P-wave traveltime in layered transversely isotropic mediaAbedi, M.M.Pardo, D.http://hdl.handle.net/20.500.11824/13242021-09-07T01:00:22Z2021-05-01T00:00:00ZLarge-offset P-wave traveltime in layered transversely isotropic media
Abedi, M.M.; Pardo, D.
Large-offset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with a vertical symmetry axis, the accuracy of traditional traveltime approximations is limited to near offsets. We have developed a new traveltime approximation that maintains the accuracy of classic equations around the zero offset and exhibits the correct curvilinear asymptote at infinitely large offsets. Our approximation is based on the conventional acoustic assumption. Its equation incorporates six parameters. To define them, we use the Taylor series expansion of the exact traveltime around the zero offset and a new asymptotic series for the infinite offset. Our asymptotic equation indicates that the traveltime behavior at infinitely large offsets is dominated by the properties of the layer with the maximum horizontal velocity in the sequence. The parameters of our approximation depend on the effective zero-offset traveltime, the normal moveout velocity, the anellipticity, a new large-offset heterogeneity parameter, and the properties of the layer with the maximum horizontal velocity in the sequence. We have applied our traveltime approximation (1) to directly calculate traveltime and ray parameter at given offsets, as analytical forward modeling, and (2) to estimate the first four of the aforementioned parameters for the layers beneath a known high-velocity layer. Our large-offset heterogeneity parameter includes the layering effect on the reflections’ traveltime.
2021-05-01T00:00:00ZMetallic microswimmers driven up the wall by gravityBrosseau, QuentinBalboa, F.Lushi, EnkeleidaWu, YangRistroph, LeifWard, Michael D.Shelley, Michael J.Zhang, Junhttp://hdl.handle.net/20.500.11824/13122021-07-30T01:00:33Z2021-07-21T00:00:00ZMetallic microswimmers driven up the wall by gravity
Brosseau, Quentin; Balboa, F.; Lushi, Enkeleida; Wu, Yang; Ristroph, Leif; Ward, Michael D.; Shelley, Michael J.; Zhang, Jun
Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show that tail-heavy swimmers preferentially orient upwards and ascend along inclined planes. We show that such gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even ultraheavy microswimmers to climb nearly vertical surfaces. Theory and simulations show that the buoyancy or gravitational torque that tends to align the rods is reinforced by a fore-aft drag asymmetry induced by hydrodynamic interactions with the wall.
2021-07-21T00:00:00ZOn isoptics and isochordal-viewed curvesRochera, D.http://hdl.handle.net/20.500.11824/13092021-07-17T01:00:33Z2021-01-01T00:00:00ZOn isoptics and isochordal-viewed curves
Rochera, D.
In this paper, some results involving isoptic curves and constant $\phi$-width curves are given for any closed curve. The non-convex case, as well as non-simple shapes with or without cusps are considered. Relating the construction of isoptics to the construction given in Holditch’s theorem, a kind of curves is defined: the isochordal-viewed curves. The explicit expression of these curves is given together with some examples. Integral formulae on the area of their isoptics are obtained and a Barbier-type theorem is derived. Finally, a characterization for isochordal-viewed hedgehogs and curves of constant $\phi$-width is given in terms of an angle function.
2021-01-01T00:00:00Z