Part 21 Report - 1997-052
ACCESSION #: 9702120348
Information & Support Services
P.O. Box 3707
Seattle, WA 98124-2207
February 3, 1997
Document Control Desk
United States Nuclear Regulatory Commission
Washington, D.C. 20555
Reference: a) Boeing Letter G-1151-RSO-92-365 dated August 31, 1992; R.
S. Orr to the NRC Operations Center
b) NRC Letter Docket No. 99901227 dated August 12, 1992; L.
J. Norrholm to R. S. Orr; Subject: Response to 10
CFR 21 Inquiry
Dear Sir or Madam:
In accordance with the reference correspondence and 10 CFR 21, Boeing is
sending the NRC the attached error notice(s) received from our former
software suppliers. Because of unknown current addresses, the following
former customers were not notified:
Reactor Controls, Inc.
Echo Energy Consultants, Inc.
Nuclear Applications and Systems Analysis Company (Japan)
Nuclear Power Services
Error notices have been sent to our other former customers.
Very truly yours,
Sandra J. Andrews
Phone: (206) 865-6248
FAX: (206) 865-4851
Mail Stop: 7A-33, or
Enclosure(s): Reissue of ANSYS letter dated January 8;
ANSYS QA Notice QA96-09R1
ANSYS [Registered Trademark] ANSYS, Inc.
201 Johnson Road Telephone 412.746.3304
Houston, PA 15342- Facsimile 412.746.9494
January 27, 1997
Attn: Class3 Error Recipients
Attached you will find a cover letter which references the Class3
Error Reports you recently received accompanied by a letter dated January
8, 1997. There was an error in this letter that I wanted to clarify.
The original letter stated that you should have received 96-45 R1 in
1996. However, 96-45 R1 was not issued in 1996. It is just being
finalized now and will be issued shortly.
Also attached to this letter is QA Notice QA96-09 R1. It was
decided to get this report out to the customers quickly instead of
waiting for our next quarterly mailing. The enclosed letter has been
updated to include this report also.
Please discard the letter dated January 8 and place the attached one
in its place. Sorry for any confusion this may have caused.
ANSYS is a registered trademark of SAS IP
ANSYS [Registered Trademark]
January 23, 1997
Dear Class3 Error Recipient:
Enclosed you will find ANSYS Class3 Error Reports 96-47, 96-48, 96-
49, 96-50, 96-51, 96-52, 96-53 and QA Notice QA96-09 R1. This QA Notice
has been issued to further clarify the warning given in QA96-09 of
potential inaccuracy in results using the three dimensional magnetic
vector potential formulation in problems with permeable materials.
In the year 1996 the following Class3 Error Reports were issued:
Class3 Error Reports 96-01 through 96-53, 96-02 R1, 95-55 R1, 95-49 R1,
95-39 R1, 95-37 R1, 94-68 R2, 93-33 R1, 93-03 R1, and 92-25 R1. ANSYS QA
Notices QA96-01 through QA96-09 and QA96-05 R1 were also issued. ANSYS
Support Coordinator Bulletin SCB 96-01 was also issued. If you are
missing any of these reports, please contact Bonny Podolek at 412-873-
2858 and they will be provided to you.
I would like to remind you of the various ways that you can receive
Class3 error information. Quarterly, Class3 errors will be delivered by
mail to the ANSYS Support Coordinator listed on your ANSYS license
agreement. Please complete and return the attached change form if there
has been a change in personnel or an address change so that these reports
can be delivered promptly.
For users desiring access to Class3 errors on a more timely basis
you can be added to our email distribution list. To register for email
notification of reports, simply send an email request including your
email address, company name/address and ANSYS agreement number to
firstname.lastname@example.org. If you are a subscriber to email distribution,
please keep us informed of any changes in your email address by emailing
Finally, Class3 Errors and QA Notices are posted on ANSYS's Internet
HomePage. The address is http://www.ansys.com. They are located in the
ANSYS Zones section of the HomePage under Customer. The username to
enter this area is "customer" and the password is "ain1fm" (ANSYS is
number 1 for me).
For your convenience, also enclosed with this mailing you will find
ANSYS Class3 Error Summary Report Summaries sorted both by error number
and keyword for Rev. 5.2 and Release 5.3
I would like to take this opportunity to extend to you wishes for a
prosperous new year.
William J. Bryan
Quality Assurance Manager
ISO 9001 UL A3725
ISO 9001 CERTIFICATION INCLUDES
ALL COMMERCIAL PRODUCTS
ANSYS is a registered trademark of SAS IP
ANSYS QA NOTICE
NOTICE NO: QA96-09 R1
SUBJECT: ELEM62 ELEM97 MAGNETICS
QA Notice 96-09 was issued on October 22, 1996 warning users of potential
inaccuracy in results using the three-dimensional magnetic vector
potential (MVP) formulation in problems with permeable materials (i.e.,
air and iron regions). ANSYS Inc, is actively working to resolve the
accuracy issue. The intent of this notice is to update you on our
At Revision 4.4A, ANSYS introduced a state-of-the-art nodal-based 3-D MVP
formulation  in the SOLID96 element to address general three-
dimensional electromagnetic field problems with an emphasis on time-
varying field analysis. This formulation complemented our scalar
potential formulations which are primarily focused at solving
magnetostatic problems. The MVP formulation was later implemented in the
SOLID62 and SOLID97 elements.
This formulation uses a standard nodal-based degree of freedom set
containing three vector potentials in non-conducting regions and an
additional scalar potential in conducting regions. In addition, it uses
a Coulomb gauge condition on the vector potential to ensure uniqueness.
As formulated, the vector potential is assumed to be continuous in the
entire solution domain, even across material boundaries. ANSYS Inc. has
benchmarked the formulation against many problems published in the
literature with excellent success. Most of these problems are eddy
current problems with analytical solutions or experimental comparisons.
In addition, we compared three-dimensional solutions to two-dimensional
planar and axisymmetric solutions for general static, harmonic, and
transient test cases and obtained excellent agreement.
Reports of solution inaccuracy using the nodal-based MVP formulation has
recently appeared  in the literature for the case of problems
containing multiple materials (i.e. problems with air and iron).
Results from this and other references suggested only a minor inaccuracy
with the nodal-based MVP formulation. There has been no report in the
literature, to the best of our knowledge, of any major accuracy issues
with the MVP formulation. It has been suggested in the literature that a
solution to the inaccuracy problem can be found by allowing the normal
component of the vector potential to jump across the air-iron interface.
It was brought to the attention of ANSYS Inc. in the spring of 1996 that
there may be a more severe limitation in the solution accuracy of the
nodal-based MVP formulation with air-iron interfaces than had been
reported in the literature. In particular, the ANSYS Verification Manual
Problem VM 190 was solved using the MVP formulation and compared results
to the General Scalar Potential (GSP) formulation originally used in the
problem (see attachment). The calculated mmf drop in the iron domain was
severely under predicted by the MVP formulation. In addition, the
magnetic field in the iron domain appeared to be extremely low in
comparison to the GSP formulation. This solution inaccuracy was more
severe than reported for other problems in the literature, perhaps tied
to the fact that in this problem the
iron appears as a multiply-connected domain (i.e., the mmf drop is
totally contained in the iron domain).
Prompted by a question regarding solution accuracy in the 3-D MVP
formulation, we immediately undertook an extensive study of the
formulation. We first confirmed that the problem VM 190 indeed gave
inaccurate results using the MVP formulation as was reported by the
customer. We extensively reviewed our implementation of the MVP
formulation and have concluded that there is no error in the coding of
It has been proposed that our gauging method may be a source of the
error. We have tested the Coulumb gauge against an ungauged formulation
and have found little difference in the solution results. Hence we are
convinced that gauging is not the major source of solution inaccuracy.
Our next step was to study the effect of allowing the normal component of
the vector potential to jump across air-iron interfaces. This had been
reported in the literature to improve solution results . We
accomplished this by taking the standard ANSYS Rev 5.3 product and run
test cases where each element of a model was individually created with
independent node sets, then tied together with constraint equations that
allowed for continuity of the tangential component of the vector
potential across element edges, and a discontinuous normal component of
the vector potential. This in essence creates-what can be called a
nodal-based edge implementation of the MVP formulation. For the test
cases examined, we did indeed obtain excellent solutions. With the
standard nodal-based formulation, we observed again poor results. Our
observations lend credence to the fact that improved results are obtained
by allowing the normal component of the vector potential to jump across
air-iron interfaces. This also helped to confirm that our nodal-based
implementation is correct and that the inaccuracy has to do with the
continuity of the potential across air-iron interfaces.
We investigated the possibility of enhancing SOLID97 and SOLID62 with a
nodal-based edge implementation by allowing for a discontinuous normal
component of the MVP through the use of internally generated constraint
equations. This approach however would lead to large computational
inefficiencies not acceptable in a commercial environment.
Our next approach was to consider a direct edge element formulation.
Edge elements have appeared in the literature over the last several years
as an alternative method. Degrees of freedom are related to the edge of
an element rather than the nodes of an element. A sample paper
considering an edge element implementation can be found in . Most of
the work in edge elements has been directed at resolving spurious modes
in high frequency applications, not at resolving solution inaccuracies in
low frequency applications. However, the edge formulation circumvents
the MVP problem by solving for edge potentials directed along the element
edge, hence there is no component of a potential normal to air-iron
interfaces to be concerned with. In January of 1997 we successfully
implemented an edge formulation for static analysis that appears to be
very robust and accurate for air-iron problems.
ANSYS Inc. is committed to developing an accurate 3-D formulation
applicable to static, harmonic, and transient analyses. We plan a
commercial release of a new edge element formulation in the 5.4 release
of ANSYS. We are presently testing the new edge element
formulation for magnetostatic problems and developing it for eddy current
problems. At the time of this writing we are not yet able to commit the
eddy current implementation for the 5.4 release, but will make every
attempt to do so.
The edge element formulation will be far more efficient than the nodal-
based counterpart by using far fewer degrees of freedom (one degree of
freedom at each element edge rather than 3 degrees of freedom at each
node). In addition, we are implementing a Tree gauging technique that
will further reduce the, active degree of freedom set. This and other
developments lead to the following advantages for our implementation;
o The edge formulation will be more accurate and efficient than
the nodal-based MVP formulation
o We have implemented the edge element into a brick form which
will help to minimize the model size and degrees of freedom.
To the best of our knowledge, there are no other commercial
codes with brick edge elements.
o Our new brick element is much more immune to the effects of
element distortion and thus will provide accurate results for
highly distorted meshes.
o Our ICCG iterative solver is not experiencing convergence
difficulties with our edge element implementation that has been
reported in the literature.
o The new formulation constitutes a consistent link between
static and dynamic analyses, thus shortening the learning curve
and minimizing user error.
o The method does not require several solution passes as may be
required when using the scalar potential formulations in
o The method can treat any arbitrary source current distribution
irrespective of the solution geometry and material
Our long-term strategy will be to implement the edge element into wedge
and tetrahedral shapes and extend to a higher-order edge implementation.
In summary, ANSYS Inc. has had early success in developing a fully
robust 3-D formulation for static and dynamic analysis of electromagnetic
fields. Preliminary results on magnetostatic tests indicate that the new
formulation will accurately solve problems containing multiple materials
of differing permeability. Our attention now is focused on eddy current
analysis to model dynamic effects. We recommend the use of the scalar
potential formulations in SOLID96, SOLID98, and SOLID5 for general 3-D
magnetostatic problems, and in the limiting case of problems containing
non-permeable materials, the use of SOLID97 with the MVP formulation for
harmonic and transient problems.
To illustrate our progress, we have taken the Verification Manual problem
VM 1 90 originally solved using our Generalized Scalar Potential
Formulation (in SOLID98) and re-solved the problem using our nodal-based
MVP formulation and our new edge-element formulation. Table 1 compares
the solution accuracy for the three methods in terms of the mmf drop
calculated in the iron with the command macro MMF. An identical
hexahedral mesh was used for all three runs.
Table 1 MMF Calculation in Iron Region
GSP Formulation 198 Amp-turns
Edge Formulation 204 Amp-turns
MVP Formulation 1.66 Amp-turns
Table 2 compares problem size and solution statistics for the three
approaches. The Frontal Solver was used since the wavefront was
relatively small. Note the significant reduction in the active degrees
of freedom for the Edge formulation over the MVP formulation, resulting
in a wavefront similar to that of the GSP formulation.
Table 2 Solution Statistics
Method Active dof"s RMS Wavefront Solution Time
GSP Formulation 8866 241 264
Edge Formulation 18888 246 257
MVP Formulation 28404 633 866
1. Biro, O. and Preis, K. "On the Use of the Magnetic Vector Potential
in the Finite Element Analysis of Three-Dimensional Eddy Currents", IEEE
Trans Magn. Vol 25, No. 4, pp 31453159, July 1989.
2. Biro, O., Preis, K., and Richter, K., "On the Use of the Magnetic
Vector Potential in the Nodal and Edge Finite Element Analysis of 31)
Magnetostatic Problems", IEEE, Trans Magn. Vol 32, No. 3, pp. 651-654,
3. Kameari, A., "Calculation of transient 3D eddy current using edge
elements", IEEE Trans. Mag., Vol 26, pp. 466-469, March 1990.
AFFECTED VERSIONS: Revision 4.4A through Release 5.3
For general static magnetic field analysis, use the scalar potential
formulations offered in elements SOLID5, SOLID96, and SOLID98.
AUTHOR: Date: January 22, 1997
Dale F. Ostergaard
REVIEWED BY QA: Date: January 22, 1997
Willian J. Bryan
APPROVAL: Date: January 22, 1997
John A. Swanson
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