Related papers: A wavelet-Galerkin algorithm of the E/B decomposit…
Bayesian solution of an inverse problem for indirect measurement $M = AU + {\mathcal{E}}$ is considered, where $U$ is a function on a domain of $R^d$. Here $A$ is a smoothing linear operator and $ {\mathcal{E}}$ is Gaussian white noise. The…
We present a first internal delensing of CMB maps, both in temperature and polarization, using the public foreground-cleaned (SMICA) Planck 2015 maps. After forming quadratic estimates of the lensing potential, we use the corresponding…
Map-space $E$/$B$ decompositions of linear polarization are attractive for foreground and CMB analyses because they isolate the $B$-family patterns that contaminate primordial tensor searches from $E$-family patterns that trace coherent…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
We derive a general ansatz for optimizing pseudo-C_l estimators used to measure CMB anisotropy power spectra, and apply it to the recently-proposed pure pseudo-C_l formalism, to obtain an estimator which achieves near-optimal B-mode power…
Gravity waves (GW) in the early universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by…
In this paper, we address the problem of extracting all super-Gaussian source signals from a linear mixture in which (i) the number of super-Gaussian sources $K$ is less than that of sensors $M$, and (ii) there are up to $M - K$ stationary…
We consider the effectiveness of foreground cleaning in the recovery of Cosmic Microwave Background (CMB) polarization sourced by gravitational waves for tensor-to-scalar ratios in the range $0<r<0.1$. Using the planned survey area,…
The detection of B-modes in the CMB polarization pattern is a major issue in modern cosmology and must therefore be handled with analytical methods that produce reliable results. We describe a method that uses the frequency dependency of…
We investigate which practical constraints are imposed by foregrounds to the detection of the B-mode polarization generated by gravitational waves in the case of experiments of the type currently being planned. Because the B-mode signal is…
We present measurements of large-scale cosmic microwave background (CMB) E-mode polarization from the Cosmology Large Angular Scale Surveyor (CLASS) 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay…
We present the analysis of high-resolution synthetic dust polarization maps derived from large-scale simulations of magnetized multiphase interstellar turbulence carried out with the AthenaK code on the $Frontier$ exascale supercomputer at…
We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded. Our approach…
We evaluate the expected level of foreground contamination to the cosmic microwave background (CMB) polarised radiation, focusing on the diffuse emission from our own Galaxy. In particular, we perform a first attempt to simulate an all sky…
We consider stochastic semi-linear evolution equations which are driven by additive, spatially correlated, Wiener noise, and in particular consider problems of heat equation (analytic semigroup) and damped-driven wave equations (bounded…
We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic discretisation based on this new formulation is exemplified by…
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
We present an alternative analysis of CMB time ordered data (TOD) using a wavelet-based representation of the data time-frequency plane. We demonstrate that the wavelet transform decorrelates $1/f$-type Gaussian stationary noise and permits…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…