Sheila Whitman

Sheila Whitman

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Pages

Posts

Future Blog Post

less than 1 minute read

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This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.

Blog Post number 4

less than 1 minute read

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

less than 1 minute read

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 2

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 1

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

publications

research

talks

Semi-Extrapolated Finite Difference Schemes: Accuracy and Consistency

Published:

When solving partial differential equations, finite difference methods are a popular choice. Several factors come into play when choosing a finite difference method, such as stability, computational cost, accuracy, and consistency. In response to the small stability regions of explicit methods and the computational cost of implicit methods, we’ve developed a novel discretization technique (semi-extrapolation) that generates explicit schemes from implicit schemes by applying extrapolation to the implicit schemes in an unconventional fashion. Semi-extrapolating can lead to improved stabilities as compared to the stabilities of analogous explicit schemes, however, consistency and accuracy can be affected by semi-extrapolation. In our presentation, we’ll discuss our semi-extrapolation technique and introduce several semi-extrapolated discretizations of the Advection Equation and the Advection-Diffusion Equation. We’ll then analyze the consistency of these semi-extrapolated discretizations, compare their accuracies against the accuracies of several common discretizations, and discuss how stability constraints and choice of extrapolation stencil both influence the consistency and accuracy of semi-extrapolated schemes.

Accuracy and Computational Cost of Semi-Extrapolated Finite Difference Schemes

Published:

When numerically solving partial differential equations, finite difference methods are a popular choice. Several factors come into play when choosing a finite difference method, such as stability, accuracy, and computational cost. In response to the small stability regions of explicit methods and the computational cost of implicit methods, we’ve developed a novel discretization technique called semi-extrapolation. Semi-extrapolation generates explicit schemes from implicit schemes by applying extrapolation in an unconventional fashion. Semi-extrapolation can improve stability, however, we’ve also found that semi-extrapolation can have unexpected and interesting effects on accuracy. In our presentation, we’ll introduce our semi-extrapolation technique and discretize the Advection Equation and the Advection-Diffusion Equation according to semi-extrapolated and mainstream finite difference methods. Then, we’ll examine the computational costs and accuracies of semi-extrapolated methods. Included in this examination will be a comparison against the costs and accuracies of mainstream methods and a discussion regarding how stability influences the accuracy of semi-extrapolated schemes.

Learning microstructure–property relationships in materials with robust features from vision transformers

Published:

Machine learning of microstructure–property relation- ships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models for each microstructure–property relationship. We propose utilizing a pre-trained foundational vision model for the extraction of task-agnostic microstructure features and subsequent light- weight machine learning. We demonstrate our approach with a pre-trained DinoV2 model on unsupervised repre- sentation of an ensemble of two-phase microstructures and modeling of their overall elastic stiffness. Our results show the potential of foundational vision models for robust mi- crostructure representation and efficient machine learning of microstructure–property relationships without the need for expensive task-specific training or fine-tuning.

teaching

Math 107

Teaching Assistant, University of Arizona, 2021

Supported the professor in managing and supervising the classroom behavior and grading homework.

Math 107

Instructor, University of Arizona, 2022

Led lectures with approximately 30 students. Developed lesson plans, hosted office hours, and graded assignments and exams.

Math 186J

Instructor, University of Arizona, 2023

Developed lesson plans, hosted office hours, and graded assignments.

Math 112

Instructor, University of Arizona, 2023

Led lectures with approximately 30 students. Developed lesson plans, hosted office hours, and graded assignments and exams.