Tensor Mesh — Lattice Structures Under Shock, Heat, and Contact

Lattice structures absorb a lander’s shock, isolate a payload from launch, and carry heat through the swing between lunar day and night. Modeling every cell of one through an impact is usually a cluster job: a direct solver needs tens of gigabytes for a million elements. Tensor Mesh models the whole periodic lattice on one desktop, every cell resolved, on the same equations and the same mesh as the solvers engineers already trust.

THE TEST A periodic slab of body-centred-cubic lattice cells, 1,064,448 quadratic tetrahedra (6,438,528 unknowns), clamped at its base and struck by a striker, followed for 512 implicit time steps. Every solver ran the same equations on the same mesh.

THE RESULT The same answers, in a fraction of the time and memory:

84.9 s and 1.7 GB against 2,872.1 s and 53.4 GB for MUMPS with METIS: 34× faster and 31× less memory.
Same answers: at every width from 2 to 12 cells, the largest difference from MUMPS and PARDISO was 4.1×10⁻¹⁰, with the same contact nodes at every step.
1,089,994,752 elements (6,593,052,672 unknowns) in 15.8 hours and 1.8 GB on the same desktop.

Million-element lattice impact

Same impact. Same answers. A sliver of the memory.

1,064,448 elements, one desktop computer. Lower is better.

Time

Generalized-α with Newton on PARDISO (COMSOL’s documented method, rebuilt)6,352.1 s

MUMPS 5.8.2 with METIS2,872.1 s

PARDISO (oneMKL 2026.1.0)2,692.9 s

Tensor84.9 s

Peak memory

PARDISO (oneMKL 2026.1.0)67.9 GB

COMSOL’s documented method, rebuilt67.0 GB

MUMPS 5.8.2 with METIS53.4 GB

Tensor1.7 GB

34× faster · 31× less memory than MUMPS measured, one run at a time

One desktop computer, 31 October to 3 November 2026. “COMSOL’s documented method” is the solver its public manuals document, rebuilt on the same equations; COMSOL itself was not run. Exact readings.

lattice width	elements	unknowns	Tensor time	Tensor memory
12 cells	1,064,448	6,438,528	84.9 s	1.7 GB
120 cells	106,444,800	643,852,800	5,081.3 s	1.8 GB
384 cells	1,089,994,752	6,593,052,672	57,012.3 s	1.8 GB

A billion elements on one desktop

Memory held at 1.7 to 1.8 GB at every width from 2 cells to 384, a 36,864-fold range in elements. At 120 and 384 cells the model is beyond the other solvers’ memory on this computer; at the widths both can run, Tensor’s answers agree with MUMPS and PARDISO to 4.1×10⁻¹⁰.

Design studies at the pace of design

Nine impact speeds at a million elements: 83.8 s for Tensor against 17,093.9 s for PARDISO, 204× faster. A sweep of 4.7 hours takes under a minute and a half.

Time stepping to engineering accuracy

Against a converged fifth-order reference, a Radau IIA convolution quadrature brings the contact force to within 0.011% at the same time step, where the implicit midpoint rule of the impact race sits at about 2.5%.

Coupled heat and motion

Against a MOOSE application built for the same equations (MOOSE is Idaho National Laboratory’s open-source multiphysics framework): on a coupled thermoelastic cell, 6.2× and 6.4× faster at two mesh sizes, agreeing to 3.17×10⁻¹³. On a coupled slab growing from 13,664 to 163,968 quadratic tetrahedra, Tensor held at 3.1 GB at every size; MOOSE grew to 23.8 GB at six cells and reached its 26 GB process limit at nine. At six cells: 154.7 s against 1,624.8 s.

Large deformation, heat, and contact

Finite strain with two-way heat coupling, struck twice, on six grids from 2,824 to 33,888 quadratic tetrahedra: 7.78× to 9.29× faster than MOOSE, with up to 4.9× less memory, every one of 192 endpoints matched on every grid. At 1,019,464 elements Tensor finished in 13.1 hours and 5.4 GB on one processor of a cloud machine with 8 processors and 32 GB. MOOSE’s own trend, fitted on the six grids and frozen before the run, projects 5.3 to 5.7 days and 34.6 to 56.8 GB at that size.