The blog post discusses the verification of the derived 1D Helmholtz Green's function, focusing on the mathematical operations involved in confirming its validity. It explores the application of differential operators, the behavio...
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Peeter Joot is a software developer with interests in physics, math, and martial arts, sharing insights on his blog.
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This post explores the line integral specialization of the Fundamental Theorem of Geometric Calculus through various parameterizations and examples, highlighting the role of vector derivatives.
This blog post discusses the mathematical expansion of the curl of a vector field using two methods: tensor index gymnastics and geometric algebra (GA). It details the tensor expansion of the curl, utilizing the Levi-Civita tensor...
The blog post explores the application of Green's functions and geometric algebra in expressing the Cauchy integral equation. It discusses the construction of complex numbers from geometric objects, the geometric algebra equivalen...
The post discusses the derivation of the Helmholtz operator Green’s function using a Heaviside theta technique. It corrects a previous error in the contour integral derivation and presents the correct form of the Green’s function....
The post explains how to enhance a compiler to support .mlir files and demonstrates line stepping through MLIR code for effective debugging.
A debugging issue in the 'silly' programming language is explored, highlighting incorrect line number information for function calls and necessary code adjustments.
The blog post discusses the Green's functions for the 3D wave equation, providing derivations and verifications for both 1D and 2D cases. It presents the mathematical formulations and explores the properties of these functions, in...
Updates to the silly MLIR compiler include new features, improved coding style, and enhanced error reporting, showcasing a significant learning experience.
The blog post discusses the derivation of Green's functions for the spacetime gradient in electrodynamics, specifically focusing on the retarded and advanced Green's functions in 1D, 2D, and 3D cases. The author critiques their pr...
Version 8 of the silly compiler simplifies its structure and adds support for PRINT numeric-literal and ELIF statements, improving its conditional handling capabilities.
The author successfully implemented IF and ELSE support in a toy compiler using MLIR and LLVM, detailing the challenges and code structure involved.
The blog post discusses the author's experiments with C++ module support, specifically focusing on the need to import the entire standard library and the challenges faced when using the g++ and clang compilers. The author shares t...
The blog post discusses the correction of errors in the derivation of Green's functions for the 1D Helmholtz and Laplacian operators. It details the process of evaluating integrals that lead to the correct Green's functions, addre...
The post evaluates the Green's function for the 3D wave equation operator, detailing the mathematical derivation and integrals involved. It discusses the retarded and advanced solutions, using pole displacement techniques and sphe...
The post provides a detailed derivation of the 2D Green's function for the wave equation operator, utilizing an alternate pole displacement method. It outlines the mathematical steps involved in the derivation, including integrals...
The blog post discusses the derivation of the Green's functions for the 1D wave equation using Fourier transforms. It outlines the mathematical setup, including the forced wave equation and the transformation of functions. The aut...
The blog post discusses the derivation and validation of the Green's function for the 1D Laplacian operator, building on previous work with the Helmholtz operator. It includes mathematical derivations and explores the delta functi...
The post discusses the derivation and validation of the 2D Green's function for the Laplacian operator, focusing on the behavior of the Helmholtz Green's functions as the wave number approaches zero. It provides mathematical expan...
The blog post discusses the use of modules in C++ as introduced in Bjarne Stroustrup's paper '21st Century C++'. The author shares their experience with C++ modules while working on DB2, highlighting the challenges of include file...
The blog post discusses the analysis of RC and LC bandpass filters, focusing on their bandwidth and resonant frequency. The author shares a personal experience of solving filter problems with a colleague, Karl, using the loop curr...
MLIR toy compiler V5 introduces array element assignments and access, enhancing its functionality with new grammar and operational capabilities.
This post summarizes various Green's functions related to gradient operators, particularly in the context of electrodynamics. It presents mathematical expressions for Green's functions corresponding to different operators, includi...
A long-time terminal user shares their challenges and key mappings while attempting to transition to using VSCode for coding tasks.