예제: 단위를 포함하여 pdesolve 사용

함수 > 풀이 및 최적화 > 풀이 구간 함수 > 예제: 단위를 포함하여 pdesolve 사용

열전도 방정식을 풀려면 pdesolve 함수를 사용합니다.

1. 다음 입력 매개 변수를 생성합니다. nTime 및 nX는 격자선 점의 수입니다.τMax는 trange의 상한값이고 a는 계수입니다.

2. PDE 풀이 블록을 설정합니다. 열전도 방정식을 사용하고 초기 조건 세트를 추가합니다. 풀이 구간 내부에서는 단위(m)를 사용합니다.

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  <solveblock>
    <regions>
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                  <id xml:space="preserve">t</id>
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                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">xx</Subscript></Span>
                  </id>
                  <sequence>
                    <id xml:space="preserve">x</id>
                    <id xml:space="preserve">t</id>
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            <real>0</real>
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      <region id="" actualWidth="197.97000000000003" actualHeight="47.2" top="76.800000000000026" left="57.6" solve-block-category="constraint">
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              </id>
              <sequence>
                <apply>
                  <scale />
                  <real>0</real>
                  <id xml:space="preserve">m</id>
                </apply>
                <id xml:space="preserve">t</id>
              </sequence>
            </apply>
            <apply>
              <scale />
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                <neg />
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                    <scale />
                    <real>10</real>
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                      <apply>
                        <scale />
                        <real>-0.1</real>
                        <id xml:space="preserve">t</id>
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                    </apply>
                  </apply>
                </parens>
              </apply>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
              </apply>
            </apply>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
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      <region id="" actualWidth="127.37333333333335" actualHeight="47.2" top="115.20000000000003" left="57.6" solve-block-category="constraint">
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          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">x</Subscript></Span>
              </id>
              <sequence>
                <apply>
                  <scale />
                  <real>1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
                </apply>
                <id xml:space="preserve">t</id>
              </sequence>
            </apply>
            <apply>
              <scale />
              <real>0</real>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
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            </apply>
          </apply>
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          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">T</id>
              <sequence>
                <id xml:space="preserve">x</id>
                <real>0</real>
              </sequence>
            </apply>
            <real>0</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="267.43666666666672" actualHeight="44.2" top="192.00000000000006" left="38.4" solve-block-category="solver">
        <math resultRef="36">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">T</id>
            <apply>
              <id labels="KEYWORD" xml:space="preserve">Pdesolve</id>
              <sequence>
                <id labels="VARIABLE" xml:space="preserve">T</id>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                <matrix rows="2" cols="1">
                  <apply>
                    <scale />
                    <real>0</real>
                    <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
                  </apply>
                  <apply>
                    <scale />
                    <real>1</real>
                    <id labels="UNIT" xml:space="preserve">m</id>
                  </apply>
                </matrix>
                <id xml:space="preserve">t</id>
                <matrix rows="2" cols="1">
                  <real>0</real>
                  <id labels="VARIABLE" xml:space="preserve">τMax</id>
                </matrix>
              </sequence>
            </apply>
          </define>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
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  </solveblock>
</region>

3. 3D 도표에 해를 시각화하려면 CreateMesh 함수를 사용합니다.

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    <define xmlns="http://schemas.mathsoft.com/math50">
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      <apply>
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        <sequence>
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          <apply>
            <scale />
            <real>0</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <apply>
            <scale />
            <real>1</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <real>0</real>
          <id labels="VARIABLE" xml:space="preserve">τMax</id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">nX</id>
          <id labels="VARIABLE" xml:space="preserve">nTime</id>
        </sequence>
      </apply>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

4. 3D 도표를 사용하여 해를 도표화합니다.

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          </axisGrid>
          <axisLabel />
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          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
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        <yAxis start="0" end="20" rank="1">
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            <gridFrequency>5</gridFrequency>
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            <tickMarks display="true" />
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          <axisLabel />
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            <general precision="3" />
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          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
          </xyDomain>
        </yAxis>
        <zAxis start="-0.00055" end="0.00165" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <numberFormat>
            <general precision="3" />
          </numberFormat>
          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">U</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.0011441619532079339</Cell>
          <Cell>0.091956017087953423</Cell>
          <Cell>0.9957624123327542</Cell>
          <Cell>0</Cell>
          <Cell>0.32809858802063024</Cell>
          <Cell>0.94060649816846953</Cell>
          <Cell>-0.087239510212507962</Cell>
          <Cell>0</Cell>
          <Cell>-0.94464279356394487</Cell>
          <Cell>0.32680805761879472</Cell>
          <Cell>-0.029094433198413844</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0.8341587442339774</Cell>
        </Cells>
      </CameraTransformMatrix>
      <CameraType>Orthographic</CameraType>
    </plot3D>
  </plot>
</region>

5. 등고선도를 사용하여 해를 도표화합니다.