Search for: All records

Radial basis functions are typically used when discretization schemes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in solving many types of differential equations. However, the weights of the interpolated solution, used in the linear superposition of basis functions to interpolate the solution, and the actual value of the solution are completely different. In fact, these weights mix the value of the solution with the geometrical location of the nodes used to discretize the equation. In this paper, we used nodal radial basis functions, which are interpolants of the impulse function at each node inside the domain. This transformation allows to solve a linear hyperbolic partial differential equation using series expansion rather than the explicit computation of a matrix inverse. This transformation effectively yields an implicit solver which only requires the multiplication of vectors with matrices. Because the solver requires neither matrix inverse nor matrix-matrix products, this approach is numerically more stable and reduces the error by at least two orders of magnitude, compared to solvers using radial basis functions directly. Further, boundary conditions are integrated directly inside the solver, at no extra cost. The method is locally conservative, keeping the error virtually constant throughout the computation. 

A search for decays to invisible particles of Higgs bosons produced in association with a top-antitop quark pair or a vector boson, which both decay to a fully hadronic final state, has been performed using proton-proton collision data collected at$${\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}}$$$\sqrt{s}=13\text{Te}\text{V}$by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$. The 95% confidence level upper limit set on the branching fraction of the 125$$\,\text {Ge}\hspace{-.08em}\text {V}$$$\text{Ge}\text{V}$Higgs boson to invisible particles,$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$, is 0.54 (0.39 expected), assuming standard model production cross sections. The results of this analysis are combined with previous$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$searches carried out at$${\sqrt{s}=7}$$$\sqrt{s}=7$, 8, and 13$$\,\text {Te}\hspace{-.08em}\text {V}$$$\text{Te}\text{V}$in complementary production modes. The combined upper limit at 95% confidence level on$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$is 0.15 (0.08 expected).