United States Nuclear Regulatory Commission - Protecting People and the Environment

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

Nuclear Administrator

Phone: (206) 865-6248

FAX: (206) 865-4851

Mail Stop: 7A-33, or

e-mail: Sandra.Andrews@PSS.Boeing.com

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, Inc.

                              Bonny Podolek

                              Quality Assurance

                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

bpodolek@ansys.com.  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.


                                   ANSYS, Inc.

                                   William J.  Bryan

                                   Quality Assurance Manager

                                                  ANSYS, Inc.

                                             ISO 9001  UL   A3725

                                                 REGISTERED FIRM

                                         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 [1] 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 [2] 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

the formulation.

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 [2].  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 [3].  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.

Our Plan

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.

Benchmark Results

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,

May 1996.

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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