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This thesis by Viktor Linders focuses on error analysis in computational mathematics, particularly in the context of finite difference operators used in partial differential equations. It explores the SBP-SAT framework, which is designed to enhance accuracy and stability in numerical solutions by weakly imposing boundary conditions. The work addresses issues related to wave propagation and dispersion errors, proposing methods to construct SBP operators with minimal dispersion error. Additionally, it analyzes the accuracy of SBP operators near boundaries and introduces a transmission problem framework for coupling different dynamics in time. The thesis offers insights into improving numerical stability and accuracy for complex mathematical and physical problems, making it relevant for researchers and practitioners in computational mathematics and engineering.

Error analysis (Mathematics) --- Finite differences. --- Finite differences

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This thesis by Hannes Frenander focuses on developing high-order accurate numerical schemes for hyperbolic problems using finite difference operators with the Simultaneous Approximation Terms (SAT) technique. The work introduces the Multiple Penalty Technique (MPT) to improve numerical scheme performance by incorporating additional data within computational domains. It also addresses the construction of Non-Reflecting Boundary Conditions (NRBC) using Summation-By-Parts (SBP) operators to ensure stability and accuracy in infinite physical domains. The research includes theoretical analysis and numerical experiments, highlighting error bounds for wave equations. Aimed at mathematicians and computational scientists, the thesis advances methodologies for modeling complex physical phenomena.

Numerical analysis. --- Finite differences. --- Numerical analysis --- Finite differences

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Finite differences. --- Heat --- Transmission --- Mathematics.

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The finite-difference time-domain (FDTD) method has revolutionized antenna design and electromagnetics engineering. Here's a cutting-edge book that focuses on the performance optimization and engineering applications of FDTD simulation systems. Covering the latest developments in this area, this unique resource offer you expert advice on the FDTD method, hardware platforms, and network systems. Moreover the book offers guidance in distinguishing between the many different electromagnetics software packages on the market today. You also find a complete chapter dedicated to large multi-scale problem solving. This practical reference is supported with 250 illustrations, 128 equations, and 11 appendixes filled with helpful data processing techniques related to the FDTD method.

Finite differences. --- Time-domain analysis.

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Partial differential equations arise in almost all areas of science, engineering, modeling, and forecasting. During the last two decades pseudospectral methods have emerged as successful alternatives to better known computational procedures, (e.g. finite difference and finite element methods of numerical solution), in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the subject is presented using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. This book will be of interest to graduate students, scientists and engineers interested in applying pseudospectral methods to real problems.

Spectral theory (Mathematics) --- Finite differences.