Phương pháp không lưới RBF -FD sử dụng nội suy Hermite RBF giải phương trình poisson

Ngo Manh Tudng Tap chi KHOA HQC & CONG NGHE 132(02): 171-175

PHUON G PHA P KHON G LUO I RBF-FD Stf DUN G NOI SUY HERMITE

R BF GIAI PHUON G TRIN H POISSON

Trudng DH Cdng ngh§ thong tin va truyi

Ngo Man h Tifdng*

1 thong - DH Thai Nguyen

Bai bao trinh bay phUdng phap khdng ludi RBF-FD (Radial Basis Function - finite

difference) dy:a tr6n ngi suy Hermite RBF giai phuong trinh Poisson [3]. Ket qua thii

nghiem cho thay phUdng phap RBF-FD sii dung ngi suy Hermite RBF cho kit qua

tdt hdn ndi suy RBF ddn diem [4] va nghiem x^p xi ciia phuong phap ddn dilm cho

kit qua tdt hdn nghiem cua phudng phap phan tii huTu ban (FEM Finite Element

Method) trgn cac tam phan bo deu.

Tuf khoa: Ham ccf sd theo bdn kinh, phiiOng tnnh Poisson, phuong phdp sai phdn

hiiu han, phi/ctng phdp phdn tii hihi han, cac t&m phdn tdn, bdi todn Dirichlet.

1 Gioti thieu

Dau the ky XX, nhiiu phUdng phap sd da

dUdc hinh thanh va phat triln, nhu phUdng

phap sai phan hiiu ban [5], phUdng phap phan

tii hitu ban [1] v.v... Cac phUdng phap nay

dIu la cac phUdng phap ludi va da dem lai

nhiing ddng gdp Idn trong viec ling dung

phUdng phap toan hoc vao thuc tiin. Tuy

nhien, ddi vdi ldp cac bai toan thyc te cd cl,u

true hinh hgc phiic tap hoac ham cd dp dao

dong Idn thi cac phUdng phap tren chUa that

hieu qua.

NhiJng nam cudi thi ky XX da hinh thanh

phUdng phap s6 theo xu hudng mdi, dd la

phudng phap khdng ludi [7, 6, 2, 3]. Ciing nhU

cac phUdng phap ludi, ludc dd giai cac bai toan

bien bang phitOng phap khong ludi ciing difdc

tinh toan tren tap cac tam nam ben trong

mien E^^t va c^c tam nam trgn bien ds (trong

phUdng phap liidi, cac tam nay la cac niit ludi).

Tu" bg tam nky ta xip xi toan tii vi phan bang

t5 hdp cac gia tri cua ham tai cac nut:

Du{x) = y^ti;i(x)ii(xi),

i=l

trong dd vectd w = (wi, W2, ••-, w„]^ dUdc ggi

la vectd tnmg sd, tit dd dUa bai toan bien vi

giai he phUdng trinh hiiu han (khdng chda cac

dao ham) Phudng phap tim vectd trgng so

dya tren cac ham ca sd bfin kinh ggi la phUdng

phap nSi suy dti lieu phan tan vdi cac ham cd

sd ban kinh RBF - FD.

Mdi phudng phap duoc dac tnmg bdi cacli

tinh vectd trgng so. Bai bao trinh bay phUdng

phap khong ludi giai phUOng trinh Poisson

dua tren vectd trgng s6 tim dUdc nhd noi suy

Hermite RBF. Kit qua thu: nghiem cho thay

phUdng phap khdng ludi RBF-FD dya trgn nSi

suy Hermite RBF giai phUdng trinh Poisson

cho kit qua kha quan.

Bai bao gom 5 phan; Sau phin gidi thigu la

phan 2, trinh bay each rdi rac bai toan Dirich￾let vdi phuong trinh Poisson; Phan 3 mieu ta

each tinh vecto trong sd bang ndi suy Hermite

RBF; Phan 4 la phudng phap RBF-FD dua

trgn ndi suy Hermite RBF; Ph^n 5 trinh bay

thii nghiem s&.

2 R6 i ra c phu'cfng trin h Poisson tre n

ca c ta m pha n b o khon g di u

Xet bai toan Dirichlet vdi phUdng trinh

Poisson trong mign ddng Q C R'': Cho ham /

xac dinh tren miin Q va ham g xiu: dinh tren

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