numerical methods in spherical coordinates

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i was looking around for a numerical method to solve laplace's equation in spherical coordinates. i came across this article



https://www.jstage.jst.go.jp/article/jgg1949/48/12/48_12_1515/_pdf/-char/en



i couldn't understand from the article how the discretization in theta and phi coordinates was performed, and specifically if d_theta and d_phi remain constant throughout the solution space, or if they are changed to keep rd_theta and rsin(theta)*d_phi constant.



much obliged



nathan




pde numerical-methods spherical-coordinates laplacian




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    Welcome to MSE. Please read this text about how to ask a good question.
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    Jul 28 at 15:47










  • Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
    – user76284
    Jul 28 at 17:34










  • On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
    – Dylan
    Jul 30 at 10:51















up vote
-2
down vote

favorite












i was looking around for a numerical method to solve laplace's equation in spherical coordinates. i came across this article



https://www.jstage.jst.go.jp/article/jgg1949/48/12/48_12_1515/_pdf/-char/en



i couldn't understand from the article how the discretization in theta and phi coordinates was performed, and specifically if d_theta and d_phi remain constant throughout the solution space, or if they are changed to keep rd_theta and rsin(theta)*d_phi constant.



much obliged



nathan




pde numerical-methods spherical-coordinates laplacian




share|cite|improve this question















  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Jul 28 at 15:47










  • Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
    – user76284
    Jul 28 at 17:34










  • On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
    – Dylan
    Jul 30 at 10:51













up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











i was looking around for a numerical method to solve laplace's equation in spherical coordinates. i came across this article



https://www.jstage.jst.go.jp/article/jgg1949/48/12/48_12_1515/_pdf/-char/en



i couldn't understand from the article how the discretization in theta and phi coordinates was performed, and specifically if d_theta and d_phi remain constant throughout the solution space, or if they are changed to keep rd_theta and rsin(theta)*d_phi constant.



much obliged



nathan




pde numerical-methods spherical-coordinates laplacian




share|cite|improve this question











i was looking around for a numerical method to solve laplace's equation in spherical coordinates. i came across this article



https://www.jstage.jst.go.jp/article/jgg1949/48/12/48_12_1515/_pdf/-char/en



i couldn't understand from the article how the discretization in theta and phi coordinates was performed, and specifically if d_theta and d_phi remain constant throughout the solution space, or if they are changed to keep rd_theta and rsin(theta)*d_phi constant.



much obliged



nathan





pde numerical-methods spherical-coordinates laplacian





share|cite|improve this question










share|cite|improve this question




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asked Jul 28 at 15:40









nathan blanc

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  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Jul 28 at 15:47










  • Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
    – user76284
    Jul 28 at 17:34










  • On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
    – Dylan
    Jul 30 at 10:51













  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Jul 28 at 15:47










  • Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
    – user76284
    Jul 28 at 17:34










  • On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
    – Dylan
    Jul 30 at 10:51








1




1




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
Jul 28 at 15:47




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
Jul 28 at 15:47












Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
– user76284
Jul 28 at 17:34




Please use MathJax to typeset equations: math.meta.stackexchange.com/questions/5020/…
– user76284
Jul 28 at 17:34












On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
– Dylan
Jul 30 at 10:51





On the second page, Fig 1, you'll see it says "the lattice intervals are $d_r$, $rd_theta$, $rsintheta d_phi$ in the respective directions"
– Dylan
Jul 30 at 10:51
















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