These discrete operators satisfy discrete analogs of the integral identities of the differential operators on unstructured grids where vector functions are defined at the grid points, and tensor functions are d
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This ...
in this view as well as a new flow, the so called Beltrami flow that moves a gray level image under a scaled mean curvature, and also succeeds in finding a natural coupling between otherwise decoupled component-wise diffusion that was often used in the past in vector- valued image diffusion...
Operating under the assumptions of linear, isotropic materials, it utilizes a finite-difference method on a staggered grid to solve for the acoustic eigenmodes (field and frequency) of the vector-field elastic wave equation with a given propagation constant. Free, fixed, symmetry, and anti-...
and orientation-specific measures of the large-scale difference between tensors. For these tasks, we have found it advantageous to treat diffusion tensors as elements of a vector space. Linear transforms on R n constitute a vector space isomorphic to R n×n [12]. Though often viewed...
JVP's are always calculated by just two calls to apply by bumping the inputs in the direction of the tangent vector. Jacobians are constructed directly from JVP's (like in jax.jacfwd). Unfortunately, due to the black box nature of the apply function linearity is lost and there is no ...
A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier–Stokes equations is presented. The classical SD algorithm is shown to be unstable for test cases involving a multi-species gas whose thermodynamic properties depend on temperature and species ...
The indicator vector Iyi is one in element corresponding to the RSSI integer yi and zero in all other elements. Iyi is an instantaneous histogram based only on the current measurement, and ht is a weighted average of past, instantaneous histogram. Two different weighted schemes, known as exponen...
The term “rotated staggered grid” is somewhat unfortunate because assuming one spatial grid position for the stress tensor and another position for the displacement vector, it is possible to find a variety of FD schemes—depending on the order of approximation. Only in one particular case can ...
(physics) A physical phenomenon (such as force, potential or fluid velocity) that pervades a region; a mathematical model of such a phenomenon that associates each point and time with a scalar, vector or tensor quantity. Magnetic field; gravitational field; scalar field 1 Farm Cultivate by grow...