Documentation
Comprehensive guides and reference materials for the iTensor platform
Project Overview
iTensor is a comprehensive platform designed for advanced tensor calculus, magnetohydrodynamics (MHD), and differential operators in curved spacetime. It provides tools for both symbolic and numerical computations, enabling engineers and scientists to explore phenomena such as gravitational lensing, time dilation, accretion disk dynamics, and particle trajectory simulations.
The platform is highly customizable and modular, facilitating both educational use and research-grade simulations. Its unified interface allows users to manipulate tensors for applications in mathematics, physics, and engineering.
Symbolic Tensor Calculus
Leveraging SymPy, iTensor can handle algebraic tensor expressions symbolically. This means users can define tensors with symbolic components (e.g., symbols like a, b) and perform operations such as addition, multiplication, contraction, etc., obtaining results in closed-form. This is particularly useful for deriving equations related to black hole physics and general relativity.
Numerical Tensor Calculus
Using NumPy, SciPy, and optionally C/C++ extensions for high-performance computations, iTensor can perform numerical operations on tensors with real or complex data. This capability enables precise simulations of physical phenomena around black holes, including accretion disk dynamics, particle trajectories, and gravitational effects on spacetime.
Black Hole Visualization Platform
The core of iTensor now includes a powerful visualization platform for black hole physics. This platform combines advanced tensor mathematics with interactive visualizations to help users understand complex phenomena in curved spacetime. The platform supports:
- Rendering of black hole event horizons and ergospheres
- Simulation of particle trajectories near black holes
- Calculation and visualization of gravitational lensing effects
- Interactive exploration of different black hole metrics (Schwarzschild, Kerr, etc.)
- Customizable parameters for mass, spin, and observer position
Core Documentation
Getting Started
Quick introduction to set up and run your first iTensor computations, with basic examples and environment setup.
Installation Guide
Detailed instructions for installing iTensor on various platforms, including dependencies and configuration options.
Architecture Overview
Technical overview of the iTensor architecture, including component interactions, APIs, and design philosophy.
Feature Documentation
Symbolic Tensors
Documentation for symbolic tensor operations, allowing manipulation of abstract mathematical expressions.
Numerical Tensors
Guide to working with concrete numerical tensor data, optimized for computational performance.
Differential Equations
Comprehensive tools for solving ordinary and partial differential equations in physics and engineering applications.
Magnetohydrodynamics
Advanced tools for studying the dynamics of electrically conducting fluids and plasmas in physics and astrophysics.
Visualization Tools
Documentation for the interactive visualization capabilities of iTensor, including tensor field and black hole rendering.
Black Hole Visualization
Guide to using the black hole visualization features, including interactive simulations, parameter customization, and physics explanations.
Examples & Tutorials
Collection of practical examples and tutorials demonstrating iTensor capabilities with step-by-step guides.
Deployment Guide
Information on deploying iTensor in various environments, from local development to production setups.
Advanced Calculations
Documentation for tensor operations, differential geometry tools, and curved spacetime calculations for black hole physics.