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


Straight Forward Uniform Mesh Refinement

Mesh Tailoring

• select tetrahedra to berefined

• manual or automatedchoice

• perform uniformrefinement

• hanging edges emerge inthe outskirts of refinedarea


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


Applications

Automated goal-oriented refinement


Applications

A-priori refinement, e.g., transmitter/receiver location, ...


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]


3D Time-domain Electromagnetic Modelling

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