virtual_casing_jax

JAX implementation of the virtual casing principle with high-order singular quadrature.

Contents

• Overview
  • Purpose
  • Scope
  • References
• Equations
  • Virtual Casing Principle
  • Internal vs External Off-Surface
  • Kernel Formulas
  • Off-Surface Evaluation
  • Field-Period Symmetry
• Numerics
  • Grid Conventions
  • Spectral Resampling
  • Surface Differentiation and Normals
  • Field-Period Target Selection
  • Singular Quadrature
  • Implementation Notes
  • Adaptive Quadrature Resolution
• Functional API
  • Key idea
  • Example
  • Guidelines
• ComputeGradB and Autodiff
  • Overview
  • Equations (from the BIEST formulation)
  • Implementation Map
  • Reference Mapping
  • Singular Quadrature (POU + Polar + Hedgehog)
  • Autodiff Strategy
  • Performance and Memory Controls
  • Internal and Off-Surface GradB
  • Parity and Validation
  • Where GradB Is Used in Optimization
  • Limitations (Current)
• Off-Surface Evaluation
  • Equations
  • Algorithm
  • Adaptive Refinement
  • JIT-Friendly Schedule
  • Off-Surface GradB (Base vs Adaptive)
  • Validation
  • Performance Notes
  • Implementation Mapping
• Test Data
  • Overview
  • Surface Coordinates
  • Bundled Geometry Assets
  • Synthetic Loop Fields
  • Randomization and Determinism
  • API
  • Validation
• Implementation
  • Structure
  • Design Decisions
  • Compatibility with Reference Code
  • Boundary Integrals (Baseline)
  • Singular Correction (Laplace FxdU / Fxd2U)
  • Internal Field Variants
  • Off-Surface Baseline
  • Off-Surface GradB
  • Off-Surface Adaptive Refinement
• Performance
  • Baseline (Direct-Sum) Path
  • Target Blocking (2D Tiling)
  • Singular Correction
  • Rematerialization
  • Adaptive Off-Surface
  • Off-Surface GradB
  • CPU and GPU
  • Tips and Tricks
  • Performance Guide
  • Profiling and Diagnostics
• Using in SIMSOPT
  • SIMSOPT-Compatible VirtualCasing
  • Examples
  • Bundled Data
  • Direct JAX Usage
• Validation
  • Test Categories
  • Tolerance Policy
• Parity Datasets
  • Dataset Sources
  • Current Dataset Prefixes
  • Dataset Format
  • Reproduction
  • Subprocess Mode
• API
  • complete_vec_field()
  • cross_prod()
  • dot_prod()
  • fft_c2r()
  • fft_r2c()
  • grad2d()
  • normal_orientation()
  • resample()
  • rotate_toroidal()
  • surf_normal_area_elem()
  • upsample()
  • biotsavart_fx_u()
  • biotsavart_fxd_u()
  • laplace_dx_u()
  • laplace_fx_u()
  • laplace_fxd2_u()
  • laplace_fxd_u()
  • biotsavart_fx_u_eval()
  • biotsavart_fxd_u_eval()
  • computeB_offsurface_adaptive()
  • computeB_offsurface_adaptive_schedule()
  • computeB_offsurface_baseline()
  • computeGradB_offsurface_adaptive_schedule()
  • field_period_target_coords()
  • laplace_dx_u_eval()
  • laplace_dx_u_eval_singular()
  • laplace_fxd2_u_eval()
  • laplace_fxd2_u_eval_singular()
  • laplace_fxd2_u_eval_vec()
  • laplace_fxd2_u_eval_vec_singular()
  • laplace_fxd_u_eval()
  • laplace_fxd_u_eval_singular()
  • laplace_fxd_u_eval_vec()
  • laplace_fxd_u_eval_vec_singular()
  • FunctionalSetup
  • build_patch_idx()
  • build_quad_setup()
  • build_surface_coord()
  • compute_external_B_functional()
  • compute_external_B_jvp_columns_functional()
  • compute_external_B_normal_functional()
  • compute_external_B_normal_jvp_columns_functional()
  • compute_external_B_offsurf_functional()
  • compute_external_gradB_functional()
  • compute_external_gradB_offsurf_functional()
  • compute_internal_B_functional()
  • compute_internal_gradB_functional()
  • prepare_functional_setup()
  • select_patch_dim_from_geom()
  • target_surface_normal()
  • QuadSetup
  • VirtualCasingJAX
  • VirtualCasing
  • Drand48
  • SurfType
  • VirtualCasingTestData
  • magnetic_field_data()
  • magnetic_field_data_offsurf()
  • magnetic_field_grad_data()
  • surface_coordinates()
  • SingularPrecomp
  • precompute_singular()
  • select_patch_dim()
• References