Radial Basis Function Methods For Large-Scale Wave Propagation

Singular Boundary Method Analysis of Obliquely Incident Water Wave Passing through Submerged Breakwater

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

Pp: 18-29 (12)

DOI: 10.2174/9781681088983121010004

* (Excluding Mailing and Handling)

Abstract

Further to the introduction of radial basis function (RBF) methods given in Chapter 1, this chapter presents a brief description of the application of RBF to twodimensional Helmholtz problems. The background of this chapter is that, in ocean engineering, a submerged breakwater have the advantages of allowing water circulation, permitting fish passage, and providing economic protection. Therefore, such breakwaters have been widely applied to reduce the energy of transmitted water waves. Under the assumption of linear wave theory, the simulation of a water wave passing through a submerged breakwater can be simplified for solving modified Helmholtz equations. In this chapter, the analysis of an oblique incident water wave passing through a submerged breakwater is taken as the engineering background for investigating the use of the singular boundary method for two-dimensional modified Helmholtz problems. The origin intensity factors for the 2-D Laplace equation, Helmholtz equation, and modified Helmholtz equation are listed.


Keywords: Radial basis functions, Singular boundary method, Water wave propagation, Fundamental solution.

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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 <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1739834393 and j.to_date >= 1739834393 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16174) 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 <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1739834393 and j.to_date >= 1739834393 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16174) 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 <= 59689235 and j.to_ip >=59689235 )) and ((j.from_date <= 1739834393 and j.to_date >= 1739834393 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 16174)
      610μsalphaeurekaselec_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` <= 1739834393 and `b`.`banner_to_date` >= 1739834393 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.09msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3283
      • 3: 1739834393
      • 4: 1739834393
      • 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='7dad1ed5dee440433de808c0f23a4590'
      240μsalphaeurekaselec_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
        sguijhSu7cZHXtDEti7cnGOhK5p1tkJ2dmxKjcj3
        uc_cart_id
        7dad1ed5dee440433de808c0f23a4590
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/16174" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/16174
        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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        ClearShow all
        Date ↕MethodURLData
        #12025-02-17 23:19:53GET/chapter/16174112196