User Guide

In-depth, topic-oriented guides covering TensorMesh’s core concepts, design choices, and how to wield each component.

Concepts

What TensorMesh is, the FEM pipeline, and how the modules fit together.

Concepts
Meshes

Build, inspect, and load/save meshes; per-node and per-cell data.

Meshes
Elements & Quadrature

The element zoo, basis functions, quadrature rules, and ordering conventions.

Elements and Quadrature
Forms

Write weak forms in pure Python via the three assembler base classes.

Forms
Boundary Conditions

Apply Dirichlet BCs via static condensation; handle Neumann naturally.

Boundary Conditions
Sparse Solvers

Linear and nonlinear sparse solves via torch-sla — five backends, batched RHS, Newton / Picard / Anderson.

Sparse Solvers
Time Integration

Explicit and implicit-linear Runge-Kutta schemes for transient problems.

Time Integration
Batched Workflows

Three axes of batching: memory chunking, batched RHS, and ML datasets.

Batched Workflows
Differentiability

End-to-end gradients through assemble → solve, for inverse problems and topology opt.

Differentiability