 Jukka Aho
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f2b306f68e
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docs(book): Add nodal assembly and multi-GPU strategy document
New 588-line comprehensive strategic document explaining winning architecture:
Executive Summary (lines 1-19):
- Key results demonstrated on real hardware
- 9-92× CPU speedup, GPU kernel compilation, MPI working, Krylov convergence
- Multi-GPU workflow validated end-to-end
Problem: Traditional FEM doesn't scale (lines 21-59):
- v0.5.1 limitations: global matrix O(N²) memory, direct solver O(N³) time
- Scalability ceiling ~100K DOF
- Cannot scale: memory N², time N³
Solution: Nodal + Matrix-Free + Multi-GPU (lines 61-193):
- Architecture diagram with MPI ranks and local GPUs
- Three pillars: nodal assembly (row-by-row), matrix-free (matvec only), multi-GPU with MPI
- Each pillar explained with code examples and advantages
Why type stability required (lines 195-241):
- GPU kernel compilation: concrete types required, abstract fails
- MPI fast path: typed buffers vs slow serialization
- Krylov solvers: matrix-free operators need concrete types
- Demonstrated with code examples
Performance characteristics (lines 243-289):
- Complexity analysis: O(N²)→O(N) memory, O(N³)→O(N·k) time
- Scalability comparison table: 10K→10M DOF
- Demonstrated results: 10×10 system, 9 iterations, 7.73×10⁻¹⁴ error
Contact mechanics killer app (lines 291-340):
- Why nodal assembly natural for contact (contact is nodal not element-based)
- Contact workflow: detect→assemble→solve→update
- Element-based assembly is mismatch for contact
Implementation strategy v1.0 (lines 342-407):
- Phase 1: Foundation (complete) - type-stable design, GPU/MPI demos, Krylov validation
- Phase 2: Core implementation - nodal assembly API, matrix-free operator, GPU accel, MPI distribution
- Phase 3: Contact integration - detection, contribution to rows, iterative solve
Comparison with other strategies (lines 409-455):
- Global matrix assembly: dead end for scalability
- Element-based matrix-free: works but suboptimal for contact
- Nodal + matrix-free + multi-GPU (ours): best for large-scale contact
Validation and evidence (lines 457-533):
- Three demonstrations: gpu_mpi_demo, krylov_mpi_gpu_demo, field_storage_comparison
- Real-world applicability: LAMMPS, GROMACS use similar patterns
- Why traditional FEM codes don't do this: legacy constraints
Conclusion (lines 535-588):
- Five validated achievements proving path forward
- Not speculation: working code on real hardware
- Path is clear: type stability foundation, nodal assembly pattern, Krylov+MPI solver
- Related documentation links
Purpose: Strategic justification for v1.0 architecture with real evidence
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2025-11-09 10:52:38 +02:00 |
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