Add section on using LLMs to CONTRIBUTING.md (#5211)

This adds a section on using LLMs to the CONTRIBUTING.md guide,
including how to connect to a MCP that knows about AMReX's
documentation.

The proposed changes:
- [ ] fix a bug or incorrect behavior in AMReX
- [ ] add new capabilities to AMReX
- [ ] changes answers in the test suite to more than roundoff level
- [ ] are likely to significantly affect the results of downstream AMReX
users
- [ ] include documentation in the code and/or rst files, if appropriate

Author: atmyers

CONTRIBUTING.md

@@ -2,7 +2,7 @@
 
 Development generally follows the following ideas:
 
-  * New features are merged into to the `development` branch using
+  * New features are merged into the `development` branch using
     Pull Requests (PRs).
 
     Nightly regression testing is used to ensure that no answers
@@ -156,15 +156,15 @@ your fork, with your `<branch_name>`.
 - It is time to communicate your changes: write a title and a description for
 your PR. People who review your PR are happy to know
   * what feature/fix you propose, and why
-  * how you made it (created a new class than inherits from...)
+  * how you made it (created a new class that inherits from...)
   * and anything relevant to your PR (performance tests, images, *etc.*)
 - Press `Create pull request`. Now you can navigate through your PR, which
 highlights the changes you made.
 
 Please DO NOT write large Pull Requests, as they are very difficult and
 time-consuming to review. As much as possible, split them into small,
 targeted PRs.
-For example, if find typos in the documentation open a pull request that only fixes typos.
+For example, if you find typos in the documentation open a pull request that only fixes typos.
 If you want to fix a bug, make a small pull request that only fixes a bug.
 If you want to implement a large feature, write helper functionality first, test it and submit those as a first pull request.
 If you want to implement a feature and are not too sure how to split it,
@@ -250,15 +250,15 @@ parenthesis of the parameter list (but not when simply calling the function). Fo
 These guidelines should be adhered to in new contributions to AMReX, but
 please refrain from making stylistic changes to unrelated sections of code in your PRs.
 
-To help developers follow the idententation and whitespace guidelines, an
+To help developers follow the indentation and whitespace guidelines, an
 [EditorConfig](https://editorconfig.org/) file is provided at
 [.editorconfig](.editorconfig).
 
 ### API Documentation Using Doxygen
 
 The Doxygen documentation is designed for advanced user-developers. It aims
 to maximize the efficiency of a search-and-find style of locating information.
-Doxygen style comment blocks should proceed the namespace, class, function, etc.
+Doxygen style comment blocks should precede the namespace, class, function, etc.
 to be documented where appropriate. For example:
 ```cpp
 /**
@@ -276,3 +276,49 @@ void MyFunction (int variable, MultiFab& data)
 ```
 Additional information regarding Doxygen comment formatting can be found
 in the [Doxygen Manual](https://www.doxygen.nl/manual/).
+
+## LLM-assisted workflows
+
+Large Language Models (LLMs) can assist with AMReX development by helping to understand the existing
+codebase, writing new code, reviewing pull requests, finding bugs, and adding tests and documentation.
+This section of the developer's guide documents how the AMReX repository is configured for LLM-based coding assistants
+and how to get the most out of them.
+
+> **_NOTE:_**  LLMs can hallucinate and sometimes produce code that compiles and runs but is incorrect. LLM-written code should
+be manually reviewed with care before opening a pull request. Please respect the AMReX maintainers' time by making sure you understand
+any bot-generated code before requesting a review.
+
+### Best Practices
+
+When working with LLM coding assistants, keep in mind that *"most best practices are based on one constraint: [the] context window fills up fast, and performance degrades as it fills"* ([Claude Code Best Practices](https://code.claude.com/docs/en/best-practices)).
+Starting from examples and iterating incrementally — as described below — helps keep sessions focused and productive.
+
+1. **Start small and iterate incrementally.**
+   Run your coding assistant inside the AMReX source directory.
+   Point the assistant to an existing function, Test, or example code and ask it modify it, gradually adding complexity and verifying along the way.
+
+2. **Write a test.**
+   Give the agent a way to verify its work. Often, the agent itself can write tests first, then implement functionality.
+
+3. **Be specific in your prompts.**
+   Reference specific files, tell the agent where to look for code patterns, and describe specific cases to test.
+
+### Connecting to a documentation Context through an MCP Server
+
+A [Model Context Protocol (MCP)](https://modelcontextprotocol.io) server is a standardized way to provide external context, such as library documentation, to LLM-based coding assistants.
+When an MCP server is configured, the assistant can query up-to-date AMReX documentation on demand, rather than relying solely on its training data. This is helpful because agents might otherwise rely on out-of-date information from their training data and/or have to read too many files into their contexts to perform development tasks.
+
+### Setting Up Context7 as an MCP Server
+
+[Context7](https://context7.com) is a service that indexes open-source project documentation and serves it through the MCP protocol.
+AMReX documentation is available at:
+
+- **AMReX**: [context7.com/amrex-codes/amrex](https://context7.com/amrex-codes/amrex)
+
+Once connected, a coding assistant (Claude Code, Cursor, VS Code Copilot, Windsurf, etc.) can retrieve relevant sections of the AMReX documentation in real time when helping you develop applications and inputs files.
+
+pyAMReX documentation is also available at:
+
+- **pyAMReX**: [context7.com/amrex-codes/pyamrex](https://context7.com/amrex-codes/pyamrex)
+
+For popular coding assistants, see the [Context7 documentation](https://context7.com/docs/resources/all-clients) to configure [AMReX](https://context7.com/amrex-codes/amrex).