⚡ Solving

Four solver backends — from CPU to GPU — with intelligent auto-detection and non-blocking execution.

Overview

Once geometry, materials, boundary conditions, and mesh are ready, ThermX assembles and solves the FEM linear system K·T = f. ThermX offers four solver backends to handle models of all sizes, with automatic selection based on hardware availability.

Available Solvers

CPU · Iterative

Conjugate Gradient

Preconditioned CG method. Scales well to large models. Runs in a Web Worker — UI stays fully responsive during solve.

Browser Desktop Non-blocking

CPU · Direct

Cholesky

Direct sparse Cholesky factorization. Exact solution, no convergence tolerance needed. Best for small models (<5k nodes).

Browser Desktop Small models

GPU · Browser

WebGPU

Preconditioned CG on the GPU using WGSL compute shaders. Uses double-single f64 emulation via vec2<f32> for ~48-bit precision. Runs in 500-iteration batches.

WebGPU Chrome / Edge GPU Accelerated

GPU · Desktop

wgpu Native

Same WGSL shaders as WebGPU, but running via the native wgpu library on Vulkan (Windows/Linux), Metal (macOS), or DirectX 12 (Windows).

wgpu Tauri Desktop Vulkan / Metal / DX12

Auto-Detection

By default, ThermX selects the best available solver automatically:

WebGPU (browser) or wgpu native (desktop) — if a compatible GPU is available
Conjugate Gradient (CPU) — fallback if no GPU is available or WebGPU is not supported
Cholesky — auto-selected for very small models regardless of GPU availability

The active solver is displayed in the Solver panel. You can override the automatic selection and force a specific solver from the dropdown.

WebGPU availability

WebGPU requires Chrome 113+ or Edge 113+. Firefox has experimental WebGPU support but it may not be enabled by default. On older browsers, ThermX automatically falls back to the CPU solver.

GPU Precision: Double-Single Emulation

GPU shaders natively operate in 32-bit float (f32), which provides only ~24 bits of mantissa precision. For FEM heat transfer, this is insufficient — small temperature differences in large models would be swallowed by rounding error.

ThermX solves this by implementing double-single (DS) arithmetic: each f64 value is represented as a pair of f32 values (vec2<f32>), giving approximately 48 bits of effective precision. This is implemented entirely in WGSL compute shaders and runs transparently on any WebGPU-capable GPU.

Solver Parameters

Parameter	Default	Description
Max iterations	10,000	CG iteration limit (GPU: runs in 500-iter batches)
Convergence tolerance	1e-8	Relative residual norm for CG convergence
Solver selection	Auto	Auto / CG / Cholesky / WebGPU / wgpu

Solve Progress

During a solve, the Solver panel shows:

Current iteration count (for iterative solvers)
Residual norm (convergence indicator) — should decrease steadily
Elapsed time
Active solver backend

The solve can be cancelled at any time without affecting the model. The UI remains fully responsive while solving runs in the background.

Convergence Issues

If the solver fails to converge within the iteration limit:

Check that all regions have materials assigned
Check that all outer edges have boundary conditions
Verify there are no isolated disconnected regions
Try increasing the max iterations or decreasing the convergence tolerance slightly
Consider switching from GPU to CPU solver for debugging (CPU solver is more numerically stable)

Tip

For large or complex models, the GPU solver can be 10–50× faster than the CPU CG solver. If you have a discrete GPU, keep the Auto setting — ThermX will use it automatically.