Search results for "Partial"
showing 10 items of 1477 documents
Robust estimation of partial directed coherence by the vector optimal parameter search algorithm
2009
We propose a method for the accurate estimation of Partial Directed Coherence (PDC) from multichannel time series. The method is based on multivariate vector autoregressive (MVAR) model identification performed through the recently proposed Vector Optimal Parameter Search (VOPS) algorithm. Using Monte Carlo simulations generated by different MVAR models, the proposed VOPS algorithm is compared with the traditional Vector Least Squares (VLS) identification method. We show that the VOPS provides more accurate PDC estimates than the VLS (either overall and single-arc errors) in presence of interactions with long delays and missing terms, and for noisy multichannel time series. ©2009 IEEE.
Adaptive Gaussian particle method for the solution of the Fokker-Planck equation
2012
The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE). A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the SODE. The decomposition as well as the propagation is subject to possibly large numeric errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error…
Numerical solution of a multi-class model for batch settling in water resource recovery facilities
2017
In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit–explicit …
A Projected Algebraic Multigrid Method for Linear Complementarity Problems
2011
We present an algebraic version of an iterative multigrid method for obstacle problems, called projected algebraic multigrid (PAMG) here. We show that classical AMG algorithms can easily be extended to deal with this kind of problem. This paves the way for efficient multigrid solution of obstacle problems with partial differential equations arising, for example, in financial engineering.
On the use of a meshless solver for PDEs governing electromagnetic transients
2009
In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.
Determining an unbounded potential for an elliptic equation with a power type nonlinearity
2022
In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results from [M. Lassas, T. Liimatainen, Y.-H. Lin, and M. Salo, Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations, Rev. Mat. Iberoam. (2021)] where this is shown for H\"older continuous potentials. Also we show that when the Dirichlet-to-Neumann map is restricted to one point on the boundary, it is possible to determine a potential $q$ in $L^{n+\varepsilon}$. The authors of arXiv:2202.0…
Boundary regularity for degenerate and singular parabolic equations
2013
We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive constant, without affecting the regularity of a boundary point. By constructing suitable families of barriers, we give some simple geometric conditions that ensure the regularity of boundary points.
The Calderón problem with partial data on manifolds and applications
2013
We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flatness condition include parts of cylindrical sets, conical sets, and surfaces of revolution. We prove local uniqueness in the Calderon problem with partial data in admissible geometries, and global uniqueness under an additional concavity assumption. This work unifies two earlier approaches to this problem (\cite{KSU} and \cite{I}) and extends both. The proofs are based on impr…
Partial data inverse problems for the Hodge Laplacian
2017
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…
Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results
2006
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are applied to hyperbolic systems of differential-geometric origin, like the sine-Gordon equation describing the surfaces of the constant negative Gaussian curvature (K-surfaces). In particular, we prove the convergence of discrete K--surfaces and their Backlund transformations to their continuous counterparts. This puts on a firm basis the generally accepted belief (which however remained unproved untill this work) that the classical differential geometry of…