Devito phase 8 [experimental - do not merge] #101
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- Change author from Langtangen & Linge to Gerard J. Gorman - Add personal acknowledgment of Langtangen's influence - Add Use of Generative AI section for transparency - Update "About this Edition" to reflect authorship
New chapters and sections: - Chapter 6: Elliptic PDEs and Iterative Solvers (Laplace, Poisson) - Chapter 7: Systems of PDEs (Shallow Water Equations) - New section in Chapter 5: Burgers Equation Key Devito patterns introduced: - Dual-buffer Function pattern for steady-state problems - Buffer swapping via argument substitution - TimeFunction pseudo-timestepping for elliptic PDEs - first_derivative() with explicit fd_order and side parameters - Multiple coupled TimeFunction objects for PDE systems - ConditionalDimension for efficient snapshot saving - Function for static fields (bathymetry) New solvers: laplace_devito.py, poisson_devito.py, burgers_devito.py, swe_devito.py New tests: 62 tests (18 elliptic, 21 burgers, 23 swe) Added Makefile for common build commands
New chapter: - Chapter 8: High-Order Methods - Dispersion Analysis (numerical dispersion, phase/group velocity) - Fornberg Algorithm (computing FD weights for arbitrary order) - Dispersion-Relation-Preserving (DRP) Schemes (Tam-Webb optimization) - Custom weights in Devito: u.dx2(weights=weights) New section in Chapter 7: - 7.3 Elastic Wave Equations - Velocity-stress formulation - VectorTimeFunction and TensorTimeFunction - Vector operators: div, grad, diag - Staggered grid discretization - Varying Lame parameters for heterogeneous media Key Devito patterns introduced: - Custom FD weights for optimized dispersion - VectorTimeFunction for velocity fields - TensorTimeFunction for stress tensors (symmetric=True) - Vector calculus operators (div, grad, diag) - Staggered grid handling for first-order systems New solvers: dispersion.py, drp_devito.py, elastic_devito.py New tests: 73 tests (39 highorder, 34 elastic) Added references for Fornberg, Tam-Webb DRP schemes
Chapter 8 additions: - Section 8.4: ADER finite difference schemes (Taylor expansion in time) - Section 8.5: Staggered grid formulations (velocity-pressure systems) Chapter 7 additions: - Section 7.4: Viscoacoustic waves with three rheological models (SLS, Kelvin-Voigt, Maxwell) - Section 7.5: 3D Viscoelastic waves with Qp/Qs attenuation New solvers: - ader_devito.py: ADER acoustic solver with high-order time stepping - staggered_devito.py: Staggered grid acoustic solver - viscoacoustic_devito.py: Three viscoacoustic models - viscoelastic_devito.py: Full 3D viscoelastic with TensorTimeFunction 91 new tests (411 total)
Chapter 9: Inverse Problems and Adjoint-State Methods - Introduction to inverse problems in seismic imaging - Adjoint-state method for gradient computation - Forward modeling with explicit SparseTimeFunction API - Reverse Time Migration (RTM) imaging condition - Full Waveform Inversion (FWI) with gradient descent - Regularization techniques (Tikhonov, Total Variation) - Least-Squares RTM with Barzilai-Borwein step length All implementations use explicit Devito API without convenience classes. New files: - chapters/adjoint/adjoint.qmd (main chapter content) - src/adjoint/forward_devito.py (explicit forward modeling) - src/adjoint/rtm_devito.py (RTM implementation) - src/adjoint/fwi_devito.py (FWI gradient computation) - src/adjoint/lsrtm_devito.py (LSRTM with Born modeling) - src/adjoint/gradient.py (gradient utilities) - tests/test_adjoint_forward.py (18 tests) - tests/test_rtm_devito.py (12 tests) - tests/test_fwi_devito.py (32 tests) - tests/test_lsrtm_devito.py (28 tests) Total tests: 501 (90 new tests for Phase 4) PDF builds successfully.
Chapter 10: Performance Optimization - Introduction to performance metrics (FLOPS, bandwidth, roofline) - Devito optimization architecture (loop blocking, SIMD, OpenMP) - GPU computing with Devito (platforms, memory management) - Performance analysis and profiling Chapter 11: Memory Management and Wavefield Storage - Memory challenges in wave propagation - Snapshotting with ConditionalDimension - Checkpointing strategies (Revolve algorithm, pyrevolve) - I/O strategies (disk, compression, HDF5) Chapter 12: Distributed Computing and Scalability - Embarrassingly parallel problems and shot-parallel workflows - Domain decomposition with MPI - Task-based parallelism with Dask - Hybrid approaches (MPI + threading, cloud) All implementations use explicit Devito API without convenience classes. New files: - chapters/performance/performance.qmd - chapters/memory/memory.qmd - chapters/distributed/distributed.qmd - src/performance/benchmark.py (benchmarking utilities) - src/memory/snapshotting.py (ConditionalDimension patterns) - src/distributed/dask_utils.py (shot-parallel workflows) - tests/test_performance.py (20 tests) - tests/test_memory.py (22 tests, 2 skip without h5py) - tests/test_distributed.py (26 tests, skip without dask) Total tests: 541 (40 new tests for Phase 5) PDF builds successfully.
New Chapters: - Chapter 13: Computational Finance (Black-Scholes PDE) - Custom SpaceDimension for asset price grid - Greeks computation (Delta, Gamma, Theta, Vega, Rho) - Analytical Black-Scholes verification - Chapter 14: Porous Media Flow (Darcy's law) - Heterogeneous permeability fields (Gaussian random, layered) - Dual-buffer Jacobi iteration with SOR - Well source terms and transient flow - Chapter 15: CFD/Navier-Stokes (Lid-driven cavity) - Fractional step/projection method - Ghia et al. (1982) benchmark data for verification - Streamfunction and vorticity computation New Source Modules: - src/finance/black_scholes_devito.py (533 lines) - src/darcy/darcy_devito.py (1003 lines) - src/cfd/navier_stokes_devito.py (739 lines) Tests: 116 new tests (657 total)
- Add Appendix D covering Lax equivalence theorem, Von Neumann stability analysis, and on-the-fly Fourier mode analysis for memory-efficient gradient computation in seismic inversion - Create src/theory/ with stability_analysis.py (CFL utilities, amplification factors) and fourier_dft.py (Devito OTF DFT implementation) - Add 38 tests for stability analysis and Fourier DFT functionality - Update _quarto.yml with new appendix and src_theory variable - Add @Witte2019 reference for OTF Fourier transform paper
Chapter 16 implementing FDTD Maxwell's equations solver: Source code (src/maxwell/): - maxwell_devito.py: 1D and 2D FDTD solvers using Devito - pml.py: Convolutional PML (CPML) absorbing boundaries - sources.py: Gaussian, sinusoidal, Ricker wavelet sources - analytical.py: Plane wave, cavity modes for verification Chapter content (chapters/maxwell/): - Maxwell's equations and curl form - Yee grid staggered field placement - Leapfrog time stepping and CFL stability - Devito implementation patterns - PEC, PMC, and ABC boundary conditions - PML theory and implementation - Examples: plane wave, resonant cavity, waveguide - 10 exercises Tests (55 new tests): - Source functions and PML coefficients - 1D/2D FDTD solver verification - Energy conservation and CFL stability - Boundary condition enforcement References: Yee1966, Taflove2005, Berenger1994, Roden2000, Mur1981
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
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Coverage 48.18% 48.18%
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Files 4 4
Lines 330 330
Branches 48 48
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Hits 159 159
Misses 158 158
Partials 13 13
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