Download - 3D Time-domain Electromagnetic Modelling
3D Time-domain ElectromagneticModellingincluding Adaptive Mesh Refinementusing a Hanging Edge approach
Carolin Schneider1, Klaus Spitzer1, Matthias Hort2
1TU Bergakademie Freiberg, 2Universität Hamburg
[email protected] vEGU 2021
Motivation
TEM Modelling in Volcanic Environments
problems: complex subsurface structures,computation time vs. resolution/accuracy, ...
solution: automated AMR using hanging edges
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 1
Simulation Workflow
Simulate electric field e on domain Ω using
PDE: ∇×∇×e+µσ∂te = 0,
Initial value: e0 = σ−1js,
Boundary Condition: n× e = 0.
Finite element discretization results in the ODE system
Ku +M∂tu = 0
u0 = b
solved by
u = e−tM−1Kb.
µ - magnetic permeability, σ - electrical conductivity, js - source current density
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 2
Straight Forward Uniform Mesh Refinement
Mesh Tailoring
• select tetrahedra to berefined
• manual or automatedchoice
• perform uniformrefinement
• hanging edges emerge inthe outskirts of refinedarea
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 3
Straight Forward Uniform Mesh Refinement
How to deal withhanging nodes and hanging edges?!
Remesh
- restructure mesh
- time consuming
Incorporation
+ automated handling
+ refinement duringsimulation run-time
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 4
Applications
Automated goal-oriented refinement
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 5
Applications
A-priori refinement, e.g., transmitter/receiver location, ...
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 6
One last slide
• Parts of this work have been funded by DFG,grant number HO 1411/29-1 | SP 356/16-1.
• Parts of this work have been presented at the GermanGeophysical Annual Meeting, DGG 2021.
• Corresponding author: Carolin [email protected]
Carolin Schneider | TU Bergakademie Freiberg | 3D TEM incl. AMR | EGU virtual General Assembly 2021 7