The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved and both the coarse meshes and the fine meshes need not be quasi-uniform. Our theory requires no assumption on the substructures which constitute the whole domain, so each substructure can be of arbitrary shape and of different size. Standard finite element interpolation from the coarse to the fine grid may be used. We consider two level overlapping Schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions.
#LARGE SYSTEM OF EQUATIONS SOLVER SOFTWARE#
A sample calculation using the MC software is then presented. These two results complete the theoretical framework for effective use of adaptive multilevel finite element methods. A number of operator properties and solvability results recently established are first summarized, making possible two quasi-optimal a priori error estimates for Galerkin approximations which are then derived. A short example is then given which involves the Hamiltonian and momentum constraints in the Einstein equations, a representative nonlinear 4-component covariant elliptic system on a Riemannian 3-manifold which arises in general relativity. Some of the more interesting features of MC are described in detail, including some new ideas for topology and geometry representation in simplex meshes, and an unusual partition of unity-based method for exploiting parallel computers. It employs a posteriori error estimation, adaptive simplex subdivision, unstructured algebraic multilevel methods, global inexact Newton methods, and numerical continuation methods for the numerical solution of nonlinear covariant elliptic systems on 2- and 3-manifolds.
#LARGE SYSTEM OF EQUATIONS SOLVER CODE#
The design of Manifold Code (MC) is then discussed MC is an adaptive multilevel finite element software package for 2- and 3-manifolds developed over several years at Caltech and UC San Diego.
Two a posteriori error indicators are derived, based on local residuals and on global linearized adjoint or dual problems. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element methods for approximating solutions to this class of problems are considered in some detail. Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. I am also totally willing to abandon this method if there is abetter one.ABSTRACT. To be clear, I'm expecting to generate coefficeints for an equation that will correct percieved distance to a contact so that it is as close as possible to the actual distance to contact. Where A is the 4 x ~1800 matrix and b is the 1 x ~1800 matrix What is the best way to solve for X, Y, Z, and A?Īlso, I'm not convinced that all of these factors are necessary, so I'm completely willing to leave out one or two of the factors.įrom the little linear algebra I understand, I've attempted something like this with no luck:Īx = b -> x = b/A via (A, b)
There seems to be a trend in the error when visualizing, so it seems to me that there should be a somewhat simple equation to correct it.Īctual_distance = perceived_distance + X(percieved_bearing) + Y(speed_over_ground) + Z(course_over_ground) + A(heading) I have a dataset including the distance and bearing to ~1800 fused radar contacts as well as the actual distance and bearing to those contacts, and I need to develop a correction equation to get the perceived values to be as close to the actual values as possible.
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