White paper · No. 01

High-fidelity at various resolution

Method: numerical · detailed 3D Package: AMD MI350-class accelerator Hardware: Apple M3 laptop Series: WarpStack white papers

Abstract

Customers usually specify a mesh — 50 µm is the common number — but resolution is something you choose: it is an input, not a result, and no single run can tell you whether the one you picked was fine enough. The question that can be checked is whether the answer still moves when you refine. On a production-class AMD MI350-class accelerator package, peak-to-peak warpage moves 6.0 µm — 0.33% across a 2.25× refinement range, and the whole deflected field is unchanged to the width of a plotted line. A resolution that runs in 11 minutes on a laptop therefore already carries the answer a ~0.9 TB, day-long 50 µm solve would return. This paper reports the convergence evidence, the surface-by-surface agreement, and the projected cost of the fine mesh we did not need to solve.

The question worth asking

Does the answer still change when you refine?

Resolution is an input, not a result, and no single run can tell you whether the one you picked was fine enough. The question worth asking is the one you can actually check: does the answer still change when you refine? On the package below, it does not — which means a resolution you can afford already carries the answer a far finer one would give.

The case — a production-class accelerator package

The package

AMD MI350-class · 8 compute dies, 2 I/O dies, 8 HBM3E stacks

1.43 M DOF

Package	64 × 72 mm
Silicon interposer	54 × 62 mm
Mechanical layers	457
Footprint regions	273
Modelled instances	138
Material entries	140
Stack height	1327 µm
Thermal load	200 → 85 °C

Plan view of the modelled package: eight teal compute dies and two I/O dies in the centre, flanked by eight purple HBM3E stacks, on a silicon interposer over a build-up substrate — The floorplan as modelledEvery die, stack and mould region resolved as its own mechanical footprint — 273 of them.

Imported from a 3Dblox description and solved as a 3D solid, layer by layer, through the full thickness of the stack — no plate approximation and no smeared effective stiffness. Eight XCD compute dies, two I/O dies and eight twelve-high HBM3E stacks, cooled from assembly to operating temperature.

The warpage

Active surface · assembly to operating temperature

1834.0 µm

Warpage map of the modelled MI350-class package — a broad symmetric dome, red and rising at the centre, falling away to deep blue at all four corners, with contour lines labelled in microns — Out-of-plane displacement · µmA symmetric dome. The centre rises 597.9 µm and the corners fall 1236.1 µm — **1834.0 µm** peak to peak.

The same answer at three resolutions

Refine it and watch

Three resolutions spanning a 2.25× range

spread 0.33%

Resolution	Degrees of freedom	Peak-to-peak
1143 µm	351,222	1828.0 µm
758 µm	703,230	1830.6 µm
507 µm	1,427,412	1834.0 µm
Spread across all three	4.1× the DOF	6.0 µm · 0.33%

Four times the degrees of freedom moves the answer by six microns on a package that bows by eighteen hundred. Counting everything — the spread above, the surface-by-surface agreement beside it, and the solver's own tolerances — total numerical uncertainty on this result is ±0.55%.

Not just the headline number

The whole surface, point by point

3.3 µm

Peak-to-peak warpage	1834.0 µm
Corners	−1236.1 µm
Centre	+597.9 µm
Largest point-by-point difference	3.3 µm · 0.18%
Total numerical uncertainty	±0.55%

A single peak-to-peak number could agree between two resolutions by coincidence. This is the whole field compared point by point along the package diagonal — the largest disagreement anywhere on the surface is 3.3 µm, less than a fifth of one percent of the bow.

Two resolutions, drawn on top of each other

Displacement along the package diagonal · 0.70 M and 1.43 M degrees of freedom

0.18% apart

Displacement along the package diagonal computed at two resolutions, plotted on top of one another and visually indistinguishable, with a residual panel below showing the difference never exceeds 3.3 microns — 758 µm mesh · 507 µm mesh · differenceTwo curves are plotted here, not one. Doubling the degrees of freedom leaves the deflected shape unchanged to the width of the line; the panel below shows the residual, which never exceeds **3.3 µm — 0.18% of peak-to-peak**.

What the finer mesh would have cost

What this run cost

The reported result, end to end

11 minutes

Resolution	507 µm
Degrees of freedom	1.43 M
Peak memory	12.5 GB
Solve time	11 min
Hardware	Apple M3 laptop

Eight cores and 24 GB — a laptop, not a cluster. All three resolutions together cost under an hour.

What 50 µm would cost

Projected from the structure of the mesh — not solved

≈0.9 TB

Resolution	Degrees of freedom	Memory
338 µm	2.7 M	23 GB
225 µm	5.7 M	50 GB
150 µm	12.4 M	109 GB
100 µm	27.2 M	239 GB
67 µm	60.2 M	530 GB
50 µm	107 M	≈0.9 TB

A 50 µm mesh on this package is 75× the degrees of freedom of the run above and needs roughly 0.9 TB of memory; solve time scales at least with degrees of freedom, putting it on the order of a day. These rows are projections, not results — none of them was solved, because the evidence above says the answer they would return is already in hand.

What this buys you

Explore coarse, commit fine. Because the answer has stopped moving well above the resolution you were told to ask for, early design work can run at a resolution that costs minutes on a laptop instead of a day on a machine you would have to buy. You spend the fine-resolution budget once, late, on the localized region that actually needs it — rather than paying it on every candidate in a sweep.

minutes, not days a laptop, not a cluster ±0.55% total numerical uncertainty the whole field, not just peak-to-peak

Scope of this study. The model is a free package body: the board, the BGA layer, the lid and any stiffener are excluded, and it includes no moisture, no cure shrinkage and no gravity. Each of those stiffens a real assembly and reduces warpage. Material properties are library values for the material classes involved, not vendor data. Production parts of this class measure substantially lower; the 1834.0 µm above is a property of the model as specified and is not a prediction of shipping hardware. What transfers to your design is the method and its cost — the agreement across resolutions, and the price of the mesh you were about to pay for. AMD, Instinct and MI350 are trademarks of Advanced Micro Devices, Inc. NoveetyAI is not affiliated with, endorsed by, or sponsored by AMD, and this study was not produced in cooperation with AMD.