Search results for "Numerical Analysis"
showing 10 items of 883 documents
Adaptive Number Knowledge in Secondary School Students: Profiles and Antecedents
2019
Cited By :1 Export Date: 10 February 2021 Correspondence Address: McMullen, J.; Department of Teacher EducationFinland; email: jake.mcmullen@utu.fi The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual…
Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
2021
Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method bas…
An elementary formula for computing shape derivatives of EFIE system matrix
2012
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in excellent agreement.
Guaranteed error control bounds for the stabilised space-time IgA approximations to parabolic problems
2017
The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their applicability. The derivation method is based on the analysis of respective integral identities and purely functional arguments. Therefore, the estimates do not contain mesh-dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they provide computable error bounds for norms associated with stabilised space-time IgA approximations as well as imply efficient error indicators enhancing the performance of fully adap…
A tribute to Massimo Lanza de Cristoforis
2020
It is with great pleasure that we dedicate the special issue Functional Analytic Methods in Partial Differential Equations of Complex Variables and Elliptic Equations to the 60th birthday of Massim...
Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study
2018
[EN] Anatomically based procedures to ablate atrial fibrillation (AF) are often successful in terminating paroxysmal AF. However, the ability to terminate persistent AF remains disappointing. New mechanistic approaches use multiple-electrode basket catheter mapping to localize and target AF drivers in the form of rotors but significant concerns remain about their accuracy. We aimed to evaluate how electrode-endocardium distance, far-field sources and inter-electrode distance affect the accuracy of localizing rotors. Sustained rotor activation of the atria was simulated numerically and mapped using a virtual basket catheter with varying electrode densities placed at different positions withi…
Accélération de la convergence et algorithme proximal
1995
Nous faisons une première étude de la question de savoir s'il est possible d'accélérer des suites issues de l'algorithme proximal ou de la méthode de l'inverse partiel par des méthodes d'extrapolation.
Numerical Methods for BVP’s Appearing in Nondestructive Ultrasonic Testing
2018
Abstract In this article we studies BVP’s that can not be solved as P.V.I or BVP with Matlab solvers ODExx or BVPxx since the solutions do not have limit in 0. We propose a numerical algorithm based on Cubic-spline written in Maple 16 [4].
Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius
2008
Recent in vitro and simulation studies have shown that guided waves measured at low ultrasound frequencies (f=200 kHz) can characterize both material properties and geometry of the cortical bone wall. In particular, a method for an accurate cortical thickness estimation from ultrasound velocity data has been presented. The clinical application remains, however, a challenge as the impact of a layer of soft tissue on top of the bone is not yet well established, and this layer is expected to affect the dispersion and relative intensities of guided modes. The present study is focused on the theoretical modeling of the impact of an overlying soft tissue. A semianalytical method and finite-differ…
Existence of dynamical low-rank approximations to parabolic problems
2021
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.