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      <div class="title_refTopic" id="xps10_pagetitle">EIGRL </div>
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      <h4 class="refClassification">Real Eigenvalue Extraction Data, Lanczos Method </h4>
      <p class="para_refTopic">Defines data needed to perform real eigenvalue (vibration or buckling) analysis with the Lanczos method. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
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               <col span="1" width="8.78*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EIGRL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">V1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">V2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ND </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MSGLVL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXSET </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SHFSCL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NORM </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="8" rowspan="1">
                     <p class="para_td">option_1 = value_1     option_2 = value_2,     etc. </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
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            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EIGRL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">3.2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">10 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="8" rowspan="1">
                     <p class="para_td">NORM=MAX     NUMS=2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
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               <col span="1" width="14.93*">
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            <thead>
               <tr>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="2" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SID </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Set identification number.  (Unique Integer&gt;0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">V1, V2 </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">For vibration analysis:  frequency range of interest.  For buckling analysis:  eigenvalue range of interest.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref86264');return(false);">65-5. </a> (Real or blank, −5 × 10<sup class="superscript">16</sup> &le; <em>V</em>1 &lt;<em>V</em>2 &le; 5. × 10<sup class="superscript">16</sup>) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">ND </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Number of roots desired.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref86264');return(false);">65-5. </a> (Integer&gt;0 or blank) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MSGLVL </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Diagnostic level.  (0 &le; Integer &le; 4; Default = 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXSET </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Number of vectors in block or set.  Default is machine dependent.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#reflF6Xp243lori');return(false);">65-15. </a></p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SHFSCL </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Estimate of the first flexible mode natural frequency.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref19350');return(false);">65-11. </a> (Real or blank) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NORM </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Method for normalizing eigenvectors (Character:  &ldquo;MASS&rdquo; or &ldquo;MAX&rdquo;) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MASS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Normalize to unit value of the generalized mass.  Not available for buckling analysis.  (Default for normal modes analysis.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAX </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Normalize to unit value of the largest displacement in the analysis set.  Displacements not in the analysis set may be larger than unity.  (Default for buckling analysis.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">ALPH </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Specifies a constant for the calculation of frequencies (Fi) at the upper boundary segments for the parallel method based on the following formula.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref67187');return(false);">65-14. </a> (Integer&gt;0.0; Default = 1.0): 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="2" rowspan="1">
                     <p align="center"><img align="bottom" src="graphics/bulkde-equ35.gif"></p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NUMS </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Number of frequency segments for the parallel method.  (Integer&gt;0; Default = 1) See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref67187');return(false);">65-14. </a></p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Fi </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Frequency at the upper boundary of the i-th segment.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref67187');return(false);">65-14. </a> (Real or blank; <em>V</em>1&lt;<em>F</em>1&lt;<em>F</em>2&lt;... <em>F</em>15&lt;<em>F</em>2) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">option_i = value_i </p>
                  </td>
                  <td align="left" colspan="2" rowspan="1">
                     <p class="para_td">Assigns a value to the fields above except for SID.  ALPH, NUMS, and Fi must be specified in this format.  V1, V2, ND, MSGLVL, MAXSET, SHFSCL, and NORM may be specified in this format as long as their corresponding field is blank in the parent entry. </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">Real eigenvalue extraction data sets must be selected with the Case Control command METHOD = SID. </p>
            </li>
            <li>
               <p class="para_item">The units of V1 and V2 are cycles per unit time in vibration analysis, and are eigenvalues in buckling analysis.  Each eigenvalue is the factor by which the prebuckling state of stress is multiplied to produce buckling in the shape defined by the corresponding eigenvector. </p>
            </li>
            <li>
               <p class="para_item">NORM = &ldquo;MASS&rdquo; is ignored in buckling analysis and NORM = &ldquo;MAX&rdquo; will be applied. </p>
            </li>
            <li>
               <p class="para_item">MAX normalization is not supported when using the gdmodes parallel solution option. It will result in incorrectly scaled eigenvectors. </p>
            </li>
            <li><a name="ref86264"></a><p class="para_item">The roots are found in order of increasing magnitude; that is, those closest to zero are found first.  The number and type of roots to be found can be determined from <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_55.html#ref80286');return(false);">Table 14-15</a>. 
               </p><a name="ref80286"></a><div class="title_tableWrapper">Table 14-15. Number and Type of Roots Found with EIGRL Entry </div>
               <table border="1" cellpadding="8" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="11.11*">
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                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">V1 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">V2 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">ND </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Number and Type of Roots Found </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V1 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">ND </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest ND or all in range, whichever is smaller. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V1 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">All in range </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V1 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">ND </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest ND in range [V1,+∞] </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V1 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest root in range [V1,+∞] </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">ND </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest ND roots in [-∞,+∞] </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest root.  See Remark 11. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">ND </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Lowest ND roots below V2 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">V2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">blank </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">All below V2 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li>
               <p class="para_item">In vibration analysis, if V1&lt;0.0, the negative eigenvalue range will be searched.  (Eigenvalues are proportional to Vi squared; therefore, the negative sign would be lost.)  This is a means for diagnosing improbable models.  In buckling analysis, negative V1 and/or V2 require no special logic. </p>
            </li>
            <li>
               <p class="para_item">Eigenvalues are sorted on order of magnitude for output.  An eigenvector is found for each eigenvalue. </p>
            </li>
            <li>
               <p class="para_item">MSGLVL controls the amount of diagnostic output during the eigenvalue extraction process.  The default value of zero suppresses all diagnostic output.  A value of one prints eigenvalues accepted at each shift.  Higher values result in increasing levels of diagnostic output. </p>
            </li>
            <li>
               <p class="para_item">MAXSET is used to limit the maximum block size.  It is otherwise set by the region size or by ND with a maximum size of 15.  It may also be reset if there is insufficient memory available.  The default value is recommended. </p>
            </li>
            <li>
               <p class="para_item">In vibration analysis, if V1 is blank, all roots less than zero are calculated.  Small negative roots are usually computational zeroes which indicate rigid body modes.  Finite negative roots are an indication of modeling problems.  If V1 is set to zero, negative eigenvalues are not calculated. </p>
            </li>
            <li><a name="ref19350"></a><p class="para_item">A specification for SHFSCL may improve performance, especially when large mass techniques are used in enforced motion analysis.  Large mass techniques can cause a large gap between the rigid body and flexible frequencies.  If this field is blank, a value for SHFSCL is estimated automatically. </p>
            </li>
            <li>
               <p class="para_item">On occasion, it may be necessary to compute more roots than requested to ensure that all roots in the range have been found. However, this method will not output the additional roots. </p>
            </li>
            <li>
               <p class="para_item">NASTRAN SYSTEM(146) provides options for I/O in sparse method only: </p><a name="ref58678"></a><div class="title_tableWrapper">Table 14-16. SYSTEM(146) Options </div>
               <table border="1" cellpadding="7" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="28.36*">
                     <col span="1" width="71.64*">
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                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">SYSTEM(146) </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Description  </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">2 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Increase memory reserved for sparse method by approximately 100%. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">3 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Increase memory reserved for sparse method by approximately 300%. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">4 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Increase memory reserved for sparse method by approximately 400%. </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li><a name="ref67187"></a><p class="para_item">For the distributed parallel method, the frequency range between V1 and V2 may be subdivided into segments that can then be analyzed in parallel.  V1 and V2 must be specified for the parallel method. NUMS must be specified greater than 1 to take advantage of the parallel method.  NUMS may also be specified on the NUMSEG keyword or the NUMSEG NASTRAN statement.  Currently, NUMSEG must equal the number of processors and by default NUMSEG is set to the number of processors requested by the DMP keyword. If both are specified, then NUMS takes precedence. </p>
               <p class="para_item">The upper frequencies of each segment may be generated automatically by ALPH or specified directly in Fi.  If both are specified, then Fi takes precedence over ALPH as long as they are consistent.  ALPH if multiplied by 100 may also be specified on FRQSEQ keyword of the NASTRAN statement. </p>
            </li>
            <li><a name="reflF6Xp243lori"></a><p class="para_item">Increasing MAXSET may improve performance for large problems where a large number of eigenvalues are being found.  The default is 7 on all machines.  SYSTEM(263) may be set in an rcfile to effectively modify the default; however the setting on the EIGRL entry always takes precedence. </p>
            </li>
            <li>
               <p class="para_item">SYSTEM(196), keyword SCRSAVE, controls reuse of scratch files when segment logic is invoked.  SYSTEM(196) is useful only when multiple frequency segments are requested on a Lanczos run.  (Multiple frequency segments can be requested via the NUMS field in the EIGRL entry and by SYSTEM(197).)  Each frequency segment requires a minimum of three scratch files.  When multiple frequency segments are used on a single processor computer then each frequency segment is solved serially.  In this case, it makes sense to let segment #2 use the scratch files which were used by segment #1 since work for segment #1 has been completed (otherwise it wouldn&rsquo;t be working on #2).  Similarly, when work for segment #2 is finished, segment #3 should be able to use #2&rsquo;s scratch files.  SYSTEM(196)=1 allows such file reuse and is considered a safe default on Version 70 and later systems. </p>
            </li>
            <li>
               <p class="para_item">The new buckling shift logic in Version 70.5 tends to shift to 1.0 first. The logic may have difficulty finding the lowest ND roots if a problem requests a small number of roots (ND) when there are thousands of roots below 1. In this case either the loading should be scaled, SHFSCL specified, or a smaller frequency range requested. </p>
            </li>
            <li>
               <p class="para_item">Because Lanczos performance is tuned for medium to large problems, this has caused difficulties with very small problems. Thus, by default, on problems with fewer than 20 degrees-of-freedom when the LAN method is selected, the method is switched to AHOU. The criteria for automatic switching is controlled by SYSTEM(359) on the NASTRAN entry. </p>
            </li>
         </ol>
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