The VOLMAX Transient Electromagnetic Modeling System, Including Sub-Cell Slots and Wires on Random Non-Orthogonal Cells Page: 1 of 11
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The VOLMAX Transient Electromagnetic Modeling System, Including
Sub-Cell Slots and Wires on Random Non-Orthogonal CellsDouglas J. Riley and C. David Turner
Radiation and Electromagnetic Analysis Department
Sandia National Laboratories, Albuquerque New Mexico 87185-1166
Internet: djriley@sandia.govDEC 0 '9 1997
O S T I1. Introduction
VOLMAX is a three-dimensional transient volumetric
Maxwell equation solver that operates on standard rec-
tilinear finite-difference time-domain (FDTD) grids,
non-orthogonal unstructured grids, or a combination of
both types (hybrid grids) [1-3]. The algorithm is fully
explicit. Open geometries are typically solved by em-
bedding multiple unstructured regions into a simple
rectilinear FDTD mesh. The grid types are fully con-
nected at the mesh interfaces without the need for com-
plex spatial interpolation. The approach permits de-
tailed modeling of complex geometry while mitigating
the large cell count typical of non-orthogonal cells such
as tetrahedral elements. To further improve efficiency,
the unstructured region carries a separate time step that
sub-cycles relative to the time-step used in the FDTD
mesh. A cross section of the interface between finite-
volume time-domain (FVTD) and FDTD grids is shown
in Fig. 1. The "wrapper layer" is a hexahedral region
that encloses the unstructured grid and provides nodal
connectivity to the surrounding FDTD mesh. The
wrapper is constructed automatically based on the un-
structured-grid topology. The unstructured region may
consist of a single rectangular block, or be of a multiple,
block-on-block form.Boundary
WRAPPER LAYER
Wrapper Inner
Boundary"
0Prim
DualI
I
I ~--
0 o -- -
--O
ary Node
NodePrimary Edge
Dual Edge-0-
--
FVTD REGION
FDTD REGIONFig. 1. The hybrid grid interface.
As shown in Fig. 1, VOLMAX is based on a staggered
grid formulation. Primary and dual grids are used.
When the unstructured grid consists exclusively of rec-
tangular hexahedral cells, the field advancement is
identically FDTD in nature, although the cells are refer-
enced in an unstructured (indirect) manner. Note that
the wrapper layer consists of rectangular cells for it's
primary grid, but the dual cells on the wrapper inner
boundary are generally non-orthogonal. As a conse-
quence, the wrapper layer is common to both the FVTD
and FDTD grids. For the case that the unstructured-grid
consists of rectangular elements, the algorithm is sec-
ond-order accurate both in space and time.
The field advancement scheme for the VOLMAX hybrid
mesh is the following. The electric fields in the FDTD
region are initially advanced based on time step, At.
On the outer boundary of the wrapper, the tangential
electric fields are second-order time interpolated to
provide a Dirichlet boundary condition for the FVTD
region. The electric and magnetic fields in the FVTD
region are advanced an integral number of sub-time
iterations relative to At,. At the completion of the sub-
cycling, the tangential electric fields on the inner
boundary of the wrapper are used to provide a Dirichlet
boundary condition to complete the magnetic-field ad-
vancement in the FDTD region. An alternative scheme
could map the magnetic fields in the wrapper layer into
the respective FDTD locations after the FDTD mag-
netic fields are advanced in time.
VOLMAX is currently integrated to the commercial
CAD package SDRC I-DEAS [4]. Solid model design,
mesh generation, and post processing are all accom-
plished through the I-DEAS interface. Electromagnetic
properties, such as voltage sources, local boundary con-
ditions, current observers, input and output ports, slots,
wires, etc., are implemented by assigning nodal attrib-
utes to the desired property. The original I-DEAS grid
file is input into the VOLMAX preprocessor, PreVol,
which builds the wrapper layer, and the primary and
dual grids. Grid construction by PreVol is accom-
plished at the rate of 50,000 to 100,000 cells/minute on
a single, high-end processor. Construction time scalesDSMTTION Or THI DQCUETr IS T..,
DTIC QUALY r7 22E ITED Ec--
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Riley, Douglas J. & Turner, C. David. The VOLMAX Transient Electromagnetic Modeling System, Including Sub-Cell Slots and Wires on Random Non-Orthogonal Cells, article, December 31, 1997; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc692510/m1/1/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.