The Fourier Singular Complement Method for the Poisson problem. Part II: axisymmetric domains

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was introduced and analysed, in prismatic domains. In this second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges or vertices of the domain, nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used

The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains

This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed, in prismatic domains. In the second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges of the domain nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used

Scan Strategy Interpolation for Laser Powder Bed Fusion in Manufacturing Applications

Laser Powder Bed Fusion (L-PBF) is a technique within additive manufacturing which uses a high power density laser to build parts from fused powdered metal alloy. This technology is well equipped to produce complex parts with otherwise impossible features such as hidden voids or lattice structures. Alongside capability, reliability and quality are key characteristics considered when choosing a manufacturing method, and these are gaining attention as this method becomes more prevalent in industry. One main indicator of a stable L-PBF process is consistent melt pool geometry, the properties of which are likely to determine the quality of the part produced. As computing power and sensing technologies become more advanced, this melt pool geometry could be studied in real time. Therefore, the loop could be closed on process monitoring in order to achieve optimal quality. This work addresses that challenge by capitalizing on machine learning techniques to reduce the latency between sending process commands and receiving process validation. This thesis presents a novel application of a k-nearest neighbor (k-NN) model to identify key parameters within melt pool imagery and predict significant process parameters. The k-NN model was trained on data provided by the National Institute of Standards and Technology (NIST). This approach was used to accurately infer the energy density of unseen layers within the same part. The algorithm was subsequently tested with unique scan strategies and found to reasonably estimate the process parameters of different parts. A 5-fold cross validation found the algorithm to be consistently predicting the class of 95.42% of the in-situ melt pool images.M.S

Illinois in the War of 1812

Review of: Illinois in the War of 1812, by Gillum Ferguson

Indian Nations of Wisconsin: Histories of Endurance and Renewal

Review of: Indian Nations of Wisconsin: Histories of Endurance and Renewal. Loew, Patty

Boone, Black Hawk, and Crockett in 1833: Unsettling the Mythic West

Review of: Boone, Black Hawk, and Crockett in 1833: Unsettling the Mythic West, edited by Michael A. Lofaro

Indian Nations of Wisconsin: Histories of Endurance and Renewal

Review of: Indian Nations of Wisconsin: Histories of Endurance and Renewal. Loew, Patty