Radial Basis Function Methods For Large-Scale Wave Propagation

RBF Based on the Modified Fundamental Solutions for High-Frequency Acoustic Problems

Author(s): Jun-Pu Li and Qing-Hua Qin

Pp: 51-68 (18)

DOI: 10.2174/9781681088983121010006

* (Excluding Mailing and Handling)

Abstract

The conception of modified fundamental solution of the 3-D Helmholtz equation is described in this chapter. Based on the modified fundamental solution, a modified singular boundary and a dual-level method of fundamental solutions are constructed. The merits of the proposed methods are that they inherit the high efficiency and accuracy of the boundary knot method and the method of fundamental solutions, whereas the high stability of the singular boundary method is not affected. For illustration, several acoustic radiation and scattering examples are investigated. Numerical experiments show that the present radial basis function (RBF) method based on the modified fundamental solutions only needs to set about 3 degrees of freedom in one wavelength per direction to produce highly accurate solutions for three-dimensional acoustic problems. At the end of this chapter, the influence of the fictitious boundary on results is analyzed in an appendix.


Keywords: Singular boundary method, Boundary knot method, Method of fundamental solutions, Sound wave propagation.

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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 316870080 and j.to_ip >=316870080 )) and ((j.from_date <= 1739835008 and j.to_date >= 1739835008 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16183) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 316870080 and j.to_ip >=316870080 )) and ((j.from_date <= 1739835008 and j.to_date >= 1739835008 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16183) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 316870080 and j.to_ip >=316870080 )) and ((j.from_date <= 1739835008 and j.to_date >= 1739835008 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16183)
      890μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3283 and `b`.`banner_from_date` <= 1739835008 and `b`.`banner_to_date` >= 1739835008 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.15msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3283
      • 3: 1739835008
      • 4: 1739835008
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='f25c5ce1657291093f0fd2045ebdb515'
      310μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    4Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        Sv232siUhwAomPcJULemFdg1xcNqnXtWiqTf32rh
        uc_cart_id
        f25c5ce1657291093f0fd2045ebdb515
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/16183" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/16183
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
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        request_cookies
        0 of 0
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        response_headers
        0 of 0
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        session_attributes
        0 of 0
        array:5 [ "_token" => "Sv232siUhwAomPcJULemFdg1xcNqnXtWiqTf32rh" "uc_cart_id" => "f25c5ce1657291093f0fd2045ebdb515" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/16183" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-17 23:30:08GET/chapter/16183112196