# Numerical Analysis and Computation Commons™

## All Articles in Numerical Analysis and Computation

1,035 full-text articles. Page 6 of 38.

2019 University of New Mexico

#### Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

##### Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension ...

2019 University of North Georgia

#### Investigations Of The Cohesion Of Nanoscale Bioactive With Titanium: A Molecular Dyanmics Approach Using Density Functional Theory And The Kohn-Sham Framework., Jerry Magaña

##### Georgia Undergraduate Research Conference (GURC)

ABSTRACT: In order to overcome the complications evolved with certain kinds of bone-replacement surgeries, especial in the field of dentistry, it has become common for manufactures of bone-prosthetic to apply a nano-scale, bioactive coating that improves the rate of integration with the host bone tissue (a process known as osseointegration). The most frequently used bio-active compound is hydroxyapite, or HaP. These coatings are applied to a titanium substrate via one of several application methods. One of the most pressing issues with these coatings is the problem of mechanical stability of the implant, which is undermined by a weaker bond between ...

Sperm Motility In Groups, 2019 California State University Maritime Academy

#### Sperm Motility In Groups, Julie Simons

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Transient Dynamics Of Infection Transmission In An Intensive Care Unit, 2019 WSU

#### Transient Dynamics Of Infection Transmission In An Intensive Care Unit, Christopher Short, Matthew S. Mietchen, Eric T. Lofgren

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

2019 Illinois State University

#### Discrete-Time Disease Model With Population Motion Under The Kolmogorov Equation View And Application, Ye Li

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

2019 Illinois State University

#### Modeling Collective Migration Of Neural Crest Cells With A Cucker-Smale Velocity Alignment Process, Claire Evensen

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

2019 George Mason University

#### Mathematical Modeling, Analysis, Simulation Of The Opioid Crisis With Prescription And Social Drug Addiction Models, Kirthi Kumar

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, 2019 George Mason University

#### Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

##### Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, 2019 University of Kufa

#### Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal

##### Karbala International Journal of Modern Science

The main contribution of this work is the development of direct explicit methods of Runge-Kutta (RK) type for solving class of seventh-order ordinary differential equations (ODEs) to improve computational efficiency. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of first-, second-, third-, fourth-, and fifth-order ODEs. Using Taylor expansion approach, we have derived the algebraic equations of the order conditions for the proposed RKM integrators up to the tenth-order. Based on these order conditions, two RKM methods of fifth- and sixth-order with four- and five-stage are derived. The zero stability of ...

2019 Brown University

#### Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner

##### Northeast Journal of Complex Systems (NEJCS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, but ...

2019 State University of New York, Suffern

#### Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen

##### Northeast Journal of Complex Systems (NEJCS)

Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as "the negative capability of being in uncertainties, mysteries, doubts." Opportunities to advance this potentiating capacity are especially abundant in constructivist ...

Creativity As An Emergent Property Of Complex Educational System, 2019 Montclair State University

#### Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya

##### Northeast Journal of Complex Systems (NEJCS)

The importance of creativity in education has been discussed often in the literature. While there remains no agreed-upon definition of creativity, the psychological literature points to traits of a creative person. These include the ability to think outside the box, make connections between seemingly disparate ideas, and question norms. The literature provides several examples of classroom experiments to help foster creativity in the classroom. In science and mathematics, we can start by getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they are not necessarily aligned with instructional practices. In this article ...

Rethinking Educational Reforms Through A Complex Dynamical Systems Approach: Preliminary Report From An Empirical Research, 2019 Aristotle University of Thessaloniki

#### Rethinking Educational Reforms Through A Complex Dynamical Systems Approach: Preliminary Report From An Empirical Research, Eugenia Tsiouplis, Dimitrios Stamovlasis

##### Northeast Journal of Complex Systems (NEJCS)

Literature on educational reforms is rich of cases where changes have been attempted, without however to attain success. Likewise the Greek education system had experienced a lot of reforms, most of which have failed to make the intended changes and they attenuated shortly after their implementation or they ceased at the stage of legislative planning. On the other hand, the traditional research have failed to develop a coherent theoretical perspective and provide satisfactory interpretations of the perpetually unsuccessful reforms. This paper is part of wider project which attempts to address the above issue following the Complex Dynamical Systems (CDS) perspective ...

Editorial Introduction To The Northeast Journal Of Complex Systems (Nejcs), 2019 Binghamton University, SUNY

#### Editorial Introduction To The Northeast Journal Of Complex Systems (Nejcs), Hiroki Sayama, Georgi Georgiev

##### Northeast Journal of Complex Systems (NEJCS)

Editorial Introduction to the Northeast Journal of Complex Systems (NEJCS)

2019 Mercy College

#### Fractality And Power Law Distributions: Shifting Perspectives In Educational Research, Matthijs Koopmans

##### Northeast Journal of Complex Systems (NEJCS)

The dynamical character of education and the complexity of its constituent relationships have long been recognized, but the full appreciation of the implications of these insights for educational research is recent. Most educational research to this day tends to focus on outcomes rather than process, and rely on conventional cross-sectional designs and statistical inference methods that do not capture this complexity. This presentation focuses on two related aspects not well accommodated by conventional models, namely fractality (self-similarity, scale invariance) and power law distributions (an inverse relationship between frequency of occurrence and strength of response). Examples are presented for both phenomena ...

Algebraic Companions And Linearizations, 2019 The University of Western Ontario

#### Algebraic Companions And Linearizations, Eunice Y. S. Chan

##### Electronic Thesis and Dissertation Repository

In this thesis, we look at a novel way of finding roots of a scalar polynomial using eigenvalue techniques. We extended this novel method to the polynomial eigenvalue problem (PEP). PEP have been used in many science and engineering applications such vibrations of structures, computer-aided geometric design, robotics, and machine learning. This thesis explains this idea in the order of which we discovered it.

In Chapter 2, a new kind of companion matrix is introduced for scalar polynomials of the form $c(\lambda) = \lambda a(\lambda)b(\lambda)+c_0$, where upper Hessenberg companions are known for the polynomials \$a(\lambda ...

Forecasting Localized Weather-Based Photovoltaic Energy Production, 2019 Southern Methodist University

#### Forecasting Localized Weather-Based Photovoltaic Energy Production, Kevin Chang, Afreen Siddiqui, Robert Slater

##### SMU Data Science Review

Photovoltaic (PV) power system performance can vary from nominal specifications when put in application, making it difficult to accurately estimate real power generation at a localized level. As the usage and efficiency of PV systems has increased in recent years, the amount of power contributed to the national power grid from solar irradiation has also increased significantly. However, solar power installations are subject to variances in efficiency and output, driven by differences in system size, local weather, and atmospheric condition changes. With a significant install base in today's world, combined with extensive solar irradiance and meteorological data, the variables ...

2019 Southern Methodist University

#### Parallel Multipole Expansion Algorithms And Their Biology Applications, Jiahui Chen

##### Mathematics Theses and Dissertations

N-body pairwise interactions are ubiquitous in scientific areas such as astrophysics, fluids mechanics, electrical engineering, molecular biology, etc. Computing these interactions using direct sum of an O(N) cost is expensive, whereas multipole expansion methods, such as the fast multipole method (FMM) or treecode, can reduce the cost to O(N) or O(N log N). This thesis focuses on developing numerical algorithms of Cartesian FMM and treecode, as well as using these algorithms to directly or implicitly solve biological problems involving pairwise interactions. This thesis consists of the following topics. 1) A cyclic parallel scheme is developed to handle ...

Assessing Computational Thinking, 2019 Australian Council for Educational Research (ACER)

#### Assessing Computational Thinking, Daniel Duckworth

##### 2009 - 2019 ACER Research Conferences

This paper provides some context for the role of computation thinking (CT) in the Australian Curriculum, an abridged literature review of CT as a problem-solving framework from the International Computer and Information Literacy Study (ICILS) 2018 assessment framework and some examples of how CT has been used to solve real-world problems. Finally, this paper presents ways to teach and assess CT.

Assessing Computational Thinking, 2019 Australian Council for Educational Research (ACER)

#### Assessing Computational Thinking, Daniel Duckworth

##### Daniel Duckworth

This paper provides some context for the role of computation thinking (CT) in the Australian Curriculum, an abridged literature review of CT as a problem-solving framework from the International Computer and Information Literacy Study (ICILS) 2018 assessment framework and some examples of how CT has been used to solve real-world problems. Finally, this paper presents ways to teach and assess CT.