Raptor — Rapid Full-Chip Power Integrity Analysis and Visualization

Validation

Measured against a direct solver

Every number below is benchmarked against a direct back-Euler transient solve on the three IBM power-grid circuits — from 54K to 1.04M nodes — over 1,001 time points, with error measured on 20 golden probe nodes per circuit. Reduction order 10, rational-Krylov shift time 1.0 s.

Runtime & accuracy — Raptor advanced Krylov vs. direct

CPU-time speedup over direct solve

Raptor (advanced Krylov) per circuit

up to 11.9×

ibmpg2t · 165K

11.86×

ibmpg3t · 1.04M

6.25×

ibmpg1t · 54K

5.57×

Direct back-Euler takes 2.3–204 s per circuit; Raptor returns the same transient in 0.41–32.6 s — an average 7.9× speedup across the three grids.

Accuracy vs. direct solve

Normalized waveform error, 20 probe nodes/circuit

<6e-6 max

Circuit	Avg error	Max error
ibmpg1t 54K	7.08e-07	5.62e-06
ibmpg2t 165K	3.30e-08	7.39e-08
ibmpg3t 1.04M	1.43e-07	7.94e-07

Errors are normalized to the waveform scale. Even the worst probe node stays under 6×10⁻⁶ — the reduced waveforms are visually indistinguishable from the direct solve.

Full comparison — direct vs. Krylov vs. Raptor

CPU time (s), speedup, and normalized error, per circuit

3 IBM grids

Circuit	Nodes	Sources	Direct CPU	Krylov CPU	Krylov ↑	Krylov max err	Raptor CPU	Raptor ↑	Raptor max err
ibmpg1t	54,265	25,082	2.267	1.510	1.50×	6.66e-14	0.407	5.57×	5.62e-06
ibmpg2t	164,897	37,168	14.097	2.947	4.78×	1.71e-13	1.189	11.86×	7.39e-08
ibmpg3t	1,043,444	202,009	203.929	54.138	3.76×	1.74e-06	32.642	6.25×	7.94e-07
Average	—	—	—	—	3.35×	—	—	7.89×	—

Reference: direct back-Euler transient. The standard Krylov method reaches machine precision (~10⁻¹⁴) at a moderate speedup; Raptor — the advanced Krylov method — is roughly 2× faster still while keeping the maximum normalized error under 6×10⁻⁶.

Accuracy & speedup — at a glance

Normalized waveform error of Raptor's advanced Krylov reduction vs. direct solve, across the three IBM power-grid circuits — **Accuracy — Raptor (advanced Krylov) vs. direct transient solve.** Average and maximum normalized waveform error, log scale, across ibmpg1t/2t/3t. Every bar sits at or below the 10⁻⁶ reference line except a single worst-case probe node at 5.6×10⁻⁶ — the reduced waveforms match the direct solve to essentially machine-grade accuracy.

Raptor CPU-time speedup over the direct back-Euler transient solve for the three IBM power-grid circuits — **CPU-time speedup — Raptor vs. direct back-Euler.** Up to 11.86× faster on ibmpg2t, and 6.25× on the million-node ibmpg3t. Under each bar: the direct-solver time collapsing to the Raptor time.

Full-chip visualization — structure, 2D drop & 3D drop

Raptor doesn't just solve the grid — it renders it. For each IBM benchmark, the metal structure, the rail-aware IR-drop / VSS-bounce map, and the same drop lifted into 3D are reconstructed from the full-node back-Euler snapshot at t = 1.0×10⁻⁸ s, straight from the SPICE geometry.

ibmpg2t · 127,565 nodes · 8 metal layers · 208,325 wire segments

Raptor 2D power-grid geometry for ibmpg2t, colored by metal layer — StructureThe full metal mesh, colored by layer (0–7) across the die.

Raptor 2D rail-aware IR-drop / VSS-bounce map for ibmpg2t — 2D dropRail-aware IR drop / VSS bounce at every node, mapped in-plane.

Raptor 3D rail-aware IR-drop / VSS-bounce surface for ibmpg2t — 3D dropThe same drop as a 3D surface — hotspots stand up off the die.

ibmpg3t · 852,536 nodes · 15 metal layers · million-node scale

Raptor 2D power-grid geometry for ibmpg3t, colored by metal layer — StructureA denser, 15-layer mesh — the largest of the IBM grids.

Raptor 2D rail-aware IR-drop / VSS-bounce map for ibmpg3t — 2D dropFull-node rail-aware IR drop across the whole million-node die.

Raptor 3D rail-aware IR-drop / VSS-bounce surface for ibmpg3t — 3D drop852K nodes lifted into 3D — the worst-case peaks read at a glance.

The bottleneck

Transient power-grid sign-off doesn't scale

Dynamic IR-drop is decided by the full time-domain response of a mesh with millions of nodes, thousands of switching current sources, and thousands of time steps. A direct solver re-solves that giant system step after step — accurate, but far too slow to keep in a design loop.

🕸️

The grid is enormous

Modern power grids reach millions of RC nodes across many metal layers. Every added node grows the linear system that must be solved at each of thousands of transient time points.

🐌

Direct transient solves crawl

Back-Euler with a sparse factorization is the trusted reference, but it re-solves the full mesh step after step. On the largest IBM grid that's over three minutes for a single run — impossible for the thousands of scenarios sign-off demands.

🔁

IR-drop must be in the loop

Floorplanning, decap budgeting, and power delivery all need dynamic-IR feedback per iteration. Without a fast, accurate transient engine, IR-drop gets checked last — when it's most expensive to fix.

The Raptor flow — netlist in, transient waveforms out

Inputs

🔌P/G netlistRC mesh · G, C, sources

⚡Current waveformsswitching PWL sources

🎯Probe nodesthe nets you care about

→

Raptor · pick the solver

Raptor · advanced Krylovrational subspace — fastest

Krylov methodstandard subspace — most accurate

→

Transient results

Node waveformsV(t) at every probe

Dynamic IR-dropworst-case droop & timing

What it does

One engine, the full transient picture

Raptor pairs an advanced Krylov subspace reduction solver with a direct back-Euler reference, delivering full transient power-grid waveforms on the very same netlist — fast enough to iterate, accurate enough to sign off. And when one machine isn't enough, a domain decomposition method scales the simulation out across CPU cores and GPUs.

TRANSIENT

📈 Full time-domain waveforms

Drive the grid with arbitrary switching-current waveforms and get the complete voltage history at every probe node — dynamic IR-drop, droop, and settling, step by step across thousands of time points.

SPEED

⚡ Up to 11.9× faster

Advanced Krylov reduction replaces the repeated full-grid solve with a tiny reduced model. Raptor returns the same transient in up to 11.9× less CPU time than a direct back-Euler solver — and the gap grows with grid size.

ACCURACY

🎯 Essentially exact

Reduced waveforms track the direct solver to a maximum normalized error under 6×10⁻⁶ — visually indistinguishable, safe for sign-off. The standard-Krylov mode reaches machine precision (≈10⁻¹⁴).

SCALE

🕸️ Million-node grids

Validated on the IBM power-grid benchmarks from 54K up to 1.04M nodes, with hundreds of thousands of switching current sources — real, published, industrial-scale meshes.

METHOD

🧮 Advanced Krylov reduction

A rational Krylov subspace captures the grid's dominant dynamics in an order-10 model that reproduces the full response — order-of-magnitude smaller than the original system, with no meaningful loss of fidelity.

EXPLORE

🔭 Built for sweeps

Once the reduced model is built, re-running new current scenarios is cheap — ideal for evaluating many power profiles, decap placements, or floorplans, or for a scriptable, closed-loop sign-off flow.

PARALLEL · DOMAIN DECOMPOSITION

🧩 Scale out across CPU cores and GPUs

For grids beyond what a single solve should carry, Raptor's domain decomposition method partitions the power grid into balanced subdomains, solves each one independently — in parallel across multi-core CPUs and GPUs — and stitches the solution back together at the shared boundary nodes. The full-grid answer, computed a piece at a time, all at once.

automatic grid partitioning independent subdomain solves multi-core CPU GPU-ready

Workflow · Raptor integration

Built for agentic EDA flows

Raptor is designed to plug directly into agentic EDA workflows. A first-class CLI and structured data interface let autonomous design agents invoke fast transient power-grid analysis, consume machine-readable waveforms and IR-drop margins, and feed those results back into floorplanning, power delivery, and decap-budgeting loops.

Fully agentic-flow aware — built to be driven by autonomous EDA agents, and to plug into any agentic flow.
First-class CLI — every analysis is scriptable from the command line; nothing in the loop needs a GUI.
Structured data interface — machine-readable netlists, node waveforms, worst-case IR-drop, and timing margins for closed-loop automation.
IR-drop-aware design iteration — agents can sweep current profiles, decap placement, and floorplans, then use Raptor results to steer the next candidate.

agentic-flow aware CLI-first structured data interface transient waveforms closed-loop sign-off

Closed-loop automation

◆ Agentic EDA flow

An autonomous agent drives floorplan, power-delivery, and decap decisions.

↓ invokes Raptor — CLI + structured data interface

▣ Raptor transient analysis

The advanced Krylov solver runs headless, producing node waveforms and dynamic IR-drop margins directly for automation.

↓ returns structured, machine-readable results

↻ Fed back to the agent

Worst-case droop, hot nets, and timing margins steer the next floorplan, decap, or power-budget iteration automatically.

Transient IR-drop analysis becomes a callable step inside your agentic EDA flow, not a hand-run GUI task.

Under the hood

Solve a tiny model, not the whole grid

The speed comes from never re-solving the full mesh. Raptor builds a compact reduced-order model that captures the grid's dominant dynamics with an advanced Krylov subspace reduction method, marches that small model through time, and projects the answer back onto the nodes you asked for. It ships in two modes that span the speed–accuracy tradeoff: Raptor, the advanced rational-Krylov solver (fastest), and the standard Krylov method (most accurate).

Read the grid

The power-grid netlist becomes its conductance and capacitance matrices plus the switching current sources — the same system a direct transient solver would march through step by step.

Build the Krylov subspace

An advanced Krylov subspace reduction method distills the grid's dominant response into a small basis. Raptor's rational variant places its expansion smartly so a tiny order-10 model captures the full dynamics.

March the reduced model

Transient integration runs on the small reduced model instead of the million-node grid — the same time steps, a fraction of the work per step. This is where the speedup comes from.

Project back to nodes

The reduced solution is projected back to the probe nodes, recovering full voltage waveforms and dynamic IR-drop that match the direct solver to machine-grade accuracy.

Raptor (advanced Krylov)

fastest

Rational Krylov subspace: expansion points chosen for the transient window. The lowest-cost path to full waveforms, still essentially exact.

up to 11.9×
speedup<6e-6
max norm. err

Krylov method

most accurate

Standard Krylov subspace reduction: reproduces the direct solver to machine precision, at a moderate but still solid speedup.

up to 4.8×
speedup~1e-14
max norm. err

Why it's fast

A direct transient solver re-solves a system with millions of unknowns at every one of thousands of time steps. Raptor instead builds a reduced model — an order-10 stand-in that behaves like the full grid over the transient window — and marches that tiny model through time. Replacing a million-node solve-per-step with a ten-variable one, then projecting back, is where the speedup comes from — with no meaningful loss of accuracy versus the direct solve.

advanced Krylov reduction rational subspace order-10 model machine-grade accuracy million-node grids reusable across sweeps domain decomposition multi-core & GPU scale-out

A direct back-Euler transient solver ships alongside as the ground-truth reference, and every Raptor result is validated against it.

Rapid Full-Chip Power Integrity Analysis and Visualization