# How can I define a MtE operator on a bounded plane?

**URL:** <https://bempp.discourse.group/t/how-can-i-define-a-mte-operator-on-a-bounded-plane/221>\
**Category:** Bempp\
**Created:** [12 December 2023 03:42 UTC](https://bempp.discourse.group/t/how-can-i-define-a-mte-operator-on-a-bounded-plane/221 "2023-12-12T03:42:42Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Yonglin](https://avatars.discourse-cdn.com/v4/letter/y/f9ae1b/32.png) [@Yonglin](https://bempp.discourse.group/u/Yonglin)\
**Post date:** [12 December 2023 03:42 UTC](https://bempp.discourse.group/t/how-can-i-define-a-mte-operator-on-a-bounded-plane/221/1 "2023-12-12T03:42:42Z")

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I want to define a MtE operator T such that

```auto
T(n × E) = n × H on Γ 

```

where Γ = { (x,y,0) | 0 \< x \< 1, 0 \< y \< 1}. (E, H) satisfies the homogeneous Maxwell equations in the upper space { z \> 0 }.

How can I do this?

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<div class="post-metadata">

**Author:** ![Elwin](https://yyz2.discourse-cdn.com/free1/user_avatar/bempp.discourse.group/elwin/32/38_2.png) [@Elwin](https://bempp.discourse.group/u/Elwin)\
**Post date:** [12 January 2024 14:53 UTC](https://bempp.discourse.group/t/how-can-i-define-a-mte-operator-on-a-bounded-plane/221/2 "2024-01-12T14:53:46Z")

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To define MtE operators, you will first have to write the operator down in terms of the electric field and magnetic field boundary operators. Then, discretize them on the geometry and take care of possible inverse operators.

Also, notice that BEMPP has functionality for free-space Green’s functions only. Half-space models are currently not supported.