Dear everyone, I am trying to figure out the specific formulation when performing C0Projection, i.e. If I define m_c0ProjectExp as following m_c0ProjectExp = MemoryManager<MultiRegions::ContField2D>:: AllocateSharedPtr(m_session,m_graph,"DefaultVar"); Then what is the specific algorithm when perform the following command(all relative options are default)? m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth); If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure? Could anyone please recommend me some materials on this? If possible, where can I find this topic on the book "Spectral/hp Element Methods for Computational Fluid Dynamics" Thank you in advance! Best wishes, Jian Yu
Hi Jain, "If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?" - You have projected your variable/field on CG Field. i.e. introduced C0 continuity across boundaries of the element. - You projected your field on a field which has C0 continuity at element boundaries. Example: -Let us assume your var is a piece-wise p1(eg:3) degree polynomial. Exactly dis-continuous at element boundaries. - Let us assume you are projecting your var on a field of p1. - if you would have used MultiRegions::DisContField2D. The two operations would not have affected your variable. .i.e. var = var_smooth, var_smooth is C^{-1}(dis-cont) at element boundaries and p1 polynomial inside each element. - Since you have used MultiRegions::ContField2D, Your var_Smooth has C0 continuity and you have p1 polynomial inside each element, but var != var_smooth. (Since you have reduced the degree of freedom). The best section to read in the book would be section 2.2 from page 21. Ashok. On Sun, Mar 26, 2017 at 2:02 PM, Jian Yu <yuj@buaa.edu.cn> wrote:
Dear everyone,
I am trying to figure out the specific formulation when performing C0Projection, i.e. If I define m_c0ProjectExp as following
m_c0ProjectExp = MemoryManager<MultiRegions::ContField2D>:: AllocateSharedPtr(m_session,m_graph,"DefaultVar");
Then what is the specific algorithm when perform the following command(all relative options are default)? m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth);
If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?
Could anyone please recommend me some materials on this? If possible, where can I find this topic on the book "Spectral/hp Element Methods for Computational Fluid Dynamics"
Thank you in advance!
Best wishes,
Jian Yu
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
Hi Ashok, Thank you very much for your reply! For m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth); The field var is obtained from a DG approximation. So var would be discontinuous across element boundaries. My question is how the FwdTrans of C0 projection handles this discontinuity or what value is used on the element boundaries such as average or maximum of the two values at the same postion of element boundaries ? Thank you! Best Jian -----原始邮件----- 发件人: "ashok jallepalli" <ash.nani@gmail.com> 发送时间: 2017年3月27日 星期一 收件人: "Jian Yu" <yuj@buaa.edu.cn> 抄送: nektar-users <nektar-users@imperial.ac.uk> 主题: [SPAM] Re: [Nektar-users] On the C0Projection Hi Jain, "If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?" - You have projected your variable/field on CG Field. i.e. introduced C0 continuity across boundaries of the element. - You projected your field on a field which has C0 continuity at element boundaries. Example: -Let us assume your var is a piece-wise p1(eg:3) degree polynomial. Exactly dis-continuous at element boundaries. - Let us assume you are projecting your var on a field of p1. - if you would have used MultiRegions::DisContField2D. The two operations would not have affected your variable. .i.e. var = var_smooth, var_smooth is C^{-1}(dis-cont) at element boundaries and p1 polynomial inside each element. - Since you have used MultiRegions::ContField2D, Your var_Smooth has C0 continuity and you have p1 polynomial inside each element, but var != var_smooth. (Since you have reduced the degree of freedom). The best section to read in the book would be section 2.2 from page 21. Ashok. On Sun, Mar 26, 2017 at 2:02 PM, Jian Yu <yuj@buaa.edu.cn> wrote: Dear everyone, I am trying to figure out the specific formulation when performing C0Projection, i.e. If I define m_c0ProjectExp as following m_c0ProjectExp = MemoryManager<MultiRegions::ContField2D>:: AllocateSharedPtr(m_session,m_graph,"DefaultVar"); Then what is the specific algorithm when perform the following command(all relative options are default)? m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth); If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure? Could anyone please recommend me some materials on this? If possible, where can I find this topic on the book "Spectral/hp Element Methods for Computational Fluid Dynamics" Thank you in advance! Best wishes, Jian Yu _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
Hi Jain, There are two commands to do FwdTrans. The first(1) does a global projection. i.e. It reduces the error L2 norm. i.e. Integral ( var- var_smooth) is minimum or Minimum energy norm (Refer "Energy norm" subsection in Section 2.2 in book.). The second(2) overwrites to one of the boundary value. (actually determined by element ID.) 1) FwdTrans 2) FwdTrans_Iter Ashok. On Mon, Mar 27, 2017 at 10:10 AM, Jian Yu <yuj@buaa.edu.cn> wrote:
Hi Ashok,
Thank you very much for your reply!
For m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth);
The field var is obtained from a DG approximation. So var would be discontinuous across element boundaries.
My question is how the FwdTrans of C0 projection handles this discontinuity or what value is used on the element boundaries such as average or maximum of the two values at the same postion of element boundaries ?
Thank you!
Best
Jian
-----原始邮件----- *发件人:* "ashok jallepalli" <ash.nani@gmail.com> *发送时间:* 2017年3月27日 星期一 *收件人:* "Jian Yu" <yuj@buaa.edu.cn> *抄送:* nektar-users <nektar-users@imperial.ac.uk> *主题:* [SPAM] Re: [Nektar-users] On the C0Projection
Hi Jain,
"If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?" - You have projected your variable/field on CG Field. i.e. introduced C0 continuity across boundaries of the element. - You projected your field on a field which has C0 continuity at element boundaries.
Example: -Let us assume your var is a piece-wise p1(eg:3) degree polynomial. Exactly dis-continuous at element boundaries. - Let us assume you are projecting your var on a field of p1. - if you would have used MultiRegions::DisContField2D. The two operations would not have affected your variable. .i.e. var = var_smooth, var_smooth is C^{-1}(dis-cont) at element boundaries and p1 polynomial inside each element. - Since you have used MultiRegions::ContField2D, Your var_Smooth has C0 continuity and you have p1 polynomial inside each element, but var != var_smooth. (Since you have reduced the degree of freedom).
The best section to read in the book would be section 2.2 from page 21.
Ashok.
On Sun, Mar 26, 2017 at 2:02 PM, Jian Yu <yuj@buaa.edu.cn> wrote:
Dear everyone,
I am trying to figure out the specific formulation when performing C0Projection, i.e. If I define m_c0ProjectExp as following
m_c0ProjectExp = MemoryManager<MultiRegions::ContField2D>:: AllocateSharedPtr(m_session,m_graph,"DefaultVar");
Then what is the specific algorithm when perform the following command(all relative options are default)? m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth);
If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?
Could anyone please recommend me some materials on this? If possible, where can I find this topic on the book "Spectral/hp Element Methods for Computational Fluid Dynamics"
Thank you in advance!
Best wishes,
Jian Yu
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
Hi Ashok., I see. That's exactly what I need. Big help! Thank you! Best Jian -----原始邮件----- 发件人: "ashok jallepalli" <ash.nani@gmail.com> 发送时间: 2017年3月28日 星期二 收件人: "Jian Yu" <yuj@buaa.edu.cn> 抄送: nektar-users <nektar-users@imperial.ac.uk> 主题: Re: [SPAM] Re: [Nektar-users] On the C0Projection Hi Jain, There are two commands to do FwdTrans. The first(1) does a global projection. i.e. It reduces the error L2 norm. i.e. Integral ( var- var_smooth) is minimum or Minimum energy norm (Refer "Energy norm" subsection in Section 2.2 in book.). The second(2) overwrites to one of the boundary value. (actually determined by element ID.) 1) FwdTrans 2) FwdTrans_Iter Ashok. On Mon, Mar 27, 2017 at 10:10 AM, Jian Yu <yuj@buaa.edu.cn> wrote: Hi Ashok, Thank you very much for your reply! For m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth); The field var is obtained from a DG approximation. So var would be discontinuous across element boundaries. My question is how the FwdTrans of C0 projection handles this discontinuity or what value is used on the element boundaries such as average or maximum of the two values at the same postion of element boundaries ? Thank you! Best Jian -----原始邮件----- 发件人: "ashok jallepalli" <ash.nani@gmail.com> 发送时间: 2017年3月27日 星期一 收件人: "Jian Yu" <yuj@buaa.edu.cn> 抄送: nektar-users <nektar-users@imperial.ac.uk> 主题: [SPAM] Re: [Nektar-users] On the C0Projection Hi Jain, "If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure?" - You have projected your variable/field on CG Field. i.e. introduced C0 continuity across boundaries of the element. - You projected your field on a field which has C0 continuity at element boundaries. Example: -Let us assume your var is a piece-wise p1(eg:3) degree polynomial. Exactly dis-continuous at element boundaries. - Let us assume you are projecting your var on a field of p1. - if you would have used MultiRegions::DisContField2D. The two operations would not have affected your variable. .i.e. var = var_smooth, var_smooth is C^{-1}(dis-cont) at element boundaries and p1 polynomial inside each element. - Since you have used MultiRegions::ContField2D, Your var_Smooth has C0 continuity and you have p1 polynomial inside each element, but var != var_smooth. (Since you have reduced the degree of freedom). The best section to read in the book would be section 2.2 from page 21. Ashok. On Sun, Mar 26, 2017 at 2:02 PM, Jian Yu <yuj@buaa.edu.cn> wrote: Dear everyone, I am trying to figure out the specific formulation when performing C0Projection, i.e.. If I define m_c0ProjectExp as following m_c0ProjectExp = MemoryManager<MultiRegions::ContField2D>:: AllocateSharedPtr(m_session,m_graph,"DefaultVar"); Then what is the specific algorithm when perform the following command(all relative options are default)? m_c0ProjectExp->FwdTrans(var,var_Coeffs); m_c0ProjectExp->BwdTrans(var_Coeffs,var_smooth); If I have a discontinuous(across element interface) distribution of var, then what has been done during the above procedure? Could anyone please recommend me some materials on this? If possible, where can I find this topic on the book "Spectral/hp Element Methods for Computational Fluid Dynamics" Thank you in advance! Best wishes, Jian Yu _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac..uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
participants (2)
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ashok jallepalli
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Jian Yu